# Chapter 3 – Time value of Money

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## Chapter 3 – Time value of Money

This chapter discusses how to calculate the present value, future value, internal rate of return, and modified internal rate of return of a cash flow stream. Understanding how (and when) to use these formulas is essential to your success as a financial manager! Formulas and examples are included with these notes.

Numbers are rounded to 4 decimal places in tables and formula. However, the actual (non-rounded) numbers are used in the calculations.
Time Value of Money Concepts

1. Time-Line Conventions

1. \$1 received today (cash inflow)

2. \$1 paid in five years (cash outflow)

3. \$1 received at the end of the third year

4. \$1 received at the beginning of the third year

5. Four-year annuity of \$1 per year, first cash flow received at t = 1 (ordinary annuity)

6. Four-year annuity of \$1 per year, first cash flow received at t = 0 (annuity due)

7. Four-year annuity of \$1 per year, first cash flow received at t = 2 (deferred annuity)

 0 1 2 3 4 5 A. \$1 B. -\$1 C. \$1 D. \$1 E. \$1 \$1 \$1 \$1 F. \$1 \$1 \$1 \$1 G. \$1 \$1 \$1 \$1

1. Notation

C0 = cash flow at time 0

C = cash flow (used when all cash flows are the same)

r = discount rate or interest rate

t = time period (e.g., t = 4), or number of years (e.g., t years in the future)

m = number of compounding periods per year (e.g., with monthly compounding, m = 12)

g = growth rate in cash flow

1. Annual Compounding, Single Payments

1. Future value of \$1 as of time 1. Interest rate = 5%.

 0 1 2 3 4 5 \$1 \$0 \$0 \$0 \$0 \$0

Formula: C0 (1 + r)t = \$1(1.05)1 = \$1.0500

Financial Calculator: N = 1, I/Y = 5, PV = -1, PMT = 0, FV = Answer
Note on financial calculators – The calculator inputs described above are for a Texas Instruments BAII Plus calculator. (Many other financial calculators require similar inputs.)
Notice that you enter a -1 as the PV and the solution is +1.05. Here is the intuition: deposit \$1 in the bank (negative cash flow), withdraw \$1.05 in one year (positive cash flow). If you had entered +1 as the PV, the solution would be –1.05.

1. Future value of \$1, as of time 5. Interest rate = 5%.

 0 1 2 3 4 5 \$1 \$0 \$0 \$0 \$0 \$0

Formula: C0 (1 + r)t = \$1(1.05)5 = \$1.2763

Financial Calculator: N = 5, I/Y = 5, PV = -1, PMT = 0, FV = Answer

1. Present value of \$1, received at time 1. Discount rate = 5%.

 0 1 2 3 4 5 \$0 \$1 \$0 \$0 \$0 \$0

Formula: C1 / (1 + r)t = \$1/(1.05)1 = \$0.9524

Financial Calculator: N = 1, I/Y = 5, PV = Answer, PMT = 0, FV = -1

1. Present value of \$1, received at time 5. Discount rate = 5%.

 0 1 2 3 4 5 \$0 \$0 \$0 \$0 \$0 \$1

Formula: C5 / (1 + r)t = \$1/(1.05)5 = \$0.7835

Financial Calculator: N = 5, I/Y = 5, PV = Answer, PMT = 0, FV = -1

1. Compounding periods less than one year

1. Future value of \$1, as of time 5. Interest rate = 5%, compounded “m” times per year.

 0 1 2 3 4 5 \$1 \$0 \$0 \$0 \$0 \$0

General (non-continuous) formula: C0 (1 + r/m)tm

Continuous compounding formula: C0 ert

Note: “e” = 2.718281828

Semi-annual compounding: \$1(1 + (0.05/2))(5)(2) = \$1.280085

Monthly compounding: \$1(1 + (0.05/12))(5)(12) = \$1.283359

Daily compounding: \$1(1 + (0.05/365))(5)(365) = \$1.284003

Continuous compounding: \$1 e(5)(0.05) = \$1.284025

Note: Some may use 360 days as the length of one year, other may take into account leap years (366 days every four years). The effects of these changes (from a 365-day year) are extremely small.
Financial Calculator (for semi-annual): N = 10, I/Y = 5/2, PV = -1, PMT = 0, FV = Answer

Financial Calculator (for monthly): N = 60, I/Y = 5/12, PV = -1, PMT = 0, FV = Answer

Financial Calculator (for daily): N = 1825, I/Y = 5/365, PV = -1, PMT = 0, FV = Answer

1. Present value of \$1, received at time 5. Discount rate = 5%, compounded m times per year.

 0 1 2 3 4 5 \$0 \$0 \$0 \$0 \$0 \$1

General (non-continuous) formula: C5 / (1 + r/m)tm

Continuous compounding formula: C5 / ert
Semi-annual compounding: \$1 / [1 + (0.05/2)](5)(2) = \$0.781198

Monthly compounding: \$1 / [1 + (0.05/12)](5)(12) = \$0.779205

Daily compounding: \$1 / [1 + (0.05/365)](5)(365) = \$0.778814

Continuous compounding: \$1 / e(5)(0.05) = \$0.778801

Financial Calculator (for semi-annual): N = 10, I/Y = 5/2, PV = Answer, PMT = 0, FV = -1

Financial Calculator (for monthly): N = 60, I/Y = 5/12, PV = Answer, PMT = 0, FV = -1

Financial Calculator (for daily): N = 1825, I/Y = 5/365, PV = Answer, PMT = 0, FV = -1

1. Constant Finite Annuities

1. Four-year annuity of \$1 per year, first cash flow received at t = 1. Interest and discount rate = 5%.

 0 1 2 3 4 5 \$0 \$1 \$1 \$1 \$1 \$0

Standard formula for the future value of a finite annuity = C [(1 + r)t – 1] / r

This standard formula for the future value of a finite annuity gives a value as of the last period of the annuity (time 4 in this example). The 1.05 is raised to the fourth power because there are 4 payments in the annuity.

 Value as of time 4 = \$1 [(1.054 – 1) / 0.05] = \$4.3101

You can calculate the value of the cash flows at other points in time by multiplying or dividing by 1+r, where r (the interest and discount rate) is 5% in this example.

For instance, assume you want to know the value of the above cash flow stream at t = 6. Time 6 is two years after time 4. To calculate, use the standard formula to determine the value at t = 4, then multiply by 1.052 to determine the value at t = 6. (Use the second power because you are calculating the value two years after time 4.) The solution is:

 Value as of time 6 = \$1 [(1.054 – 1) / 0.05] 1.052 = \$4.7519

As a second example, assume that you want to know the value of the above cash flow stream at t = 1. Time 1 is three years before time 4. To calculate, use the standard formula to determine the value at t = 4, then divide by 1.053 to determine the value at t = 1. (Use the third power because you are calculating the value three years before time 4.) The solution is:

 Value as of time 1 = \$1 [(1.054 – 1) / 0.05] / 1.053 = \$3.7232

Therefore, “multiply” when you want to determine the value at a later date, “divide” when you want to determine the value at an earlier date.

Some more examples:

 Value as of time 0 = \$1 [(1.054 – 1) / 0.05] / 1.054 = \$3.5460 Value as of time 1 = \$1 [(1.054 – 1) / 0.05] / 1.053 = \$3.7232 Value as of time 2 = \$1 [(1.054 – 1) / 0.05] / 1.052 = \$3.9094 Value as of time 3 = \$1 [(1.054 – 1) / 0.05] / 1.051 = \$4.1049 Value as of time 4 = \$1 [(1.054 – 1) / 0.05] = \$4.3101 Value as of time 5 = \$1 [(1.054 – 1) / 0.05] 1.051 = \$4.5256 Value as of time 6 = \$1 [(1.054 – 1) / 0.05] 1.052 = \$4.7519 Value as of time 7 = \$1 [(1.054 – 1) / 0.05] 1.053 = \$4.9895

Financial Calculator (time 0): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Divide answer by 1.054.

Financial Calculator (time 1): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Divide answer by 1.053.

Financial Calculator (time 2): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Divide answer by 1.052.

Financial Calculator (time 3): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Divide answer by 1.051.

Financial Calculator (time 4): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer.

Financial Calculator (time 5): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Multiply answer by 1.051.

Financial Calculator (time 6): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Multiply answer by 1.052

Financial Calculator (time 7): N = 4, I/Y = 5, PV = 0, PMT = -1, FV = Answer. Multiply answer by 1.053
You can also use the formula for the present value of a finite annuity to calculate the value of a cash flow stream at different points in time.
Standard formula for the present value of a finite annuity = C { [1 – (1 / (1 + r))t] / r}
The standard formula gives a value one period before the first payment of the annuity (time 0 in this example). The 1.05 is raised to the fourth power because there are 4 payments in the annuity.

 Value as of time 0 = \$1 { [1 – (1/1.05)4] / (0.05) } = \$3.5460

As before, you can calculate the value at other points in time by multiplying or dividing by 1+r, (1.05 in this example).

Two examples:

 Value as of time 1 = \$1 { [1 – (1/1.05)4] / (0.05) } 1.051 = \$3.7232

 Value as of time 6 = \$1 { [1 – (1/1.05)4] / (0.05) } 1.056 = \$4.7519

Financial Calculator (time 0): N = 4, I/Y = 5, PV = Answer, PMT = -1, FV = 0

Financial Calculator (time 1): N = 4, I/Y = 5, PV = Answer, PMT = -1, FV = 0. Multiply answer by 1.051.

Financial Calculator (time 6): N = 4, I/Y = 5, PV = Answer, PMT = -1, FV = 0. Multiply answer by 1.056.

1. Three-year annuity of \$1 per year, first cash flow received at t = 0. Interest and discount rate = 5%.

 0 1 2 3 4 5 \$1 \$1 \$1 \$0 \$0 \$0

The standard future value annuity formula gives a value as of the last year of the annuity (year 2 in this example). This is a three-year annuity. Therefore, 1.05 is raised to the third power in the formula.

 Value as of time 2 = \$1 [(1.053 – 1) / 0.05] = \$3.1525

The value at other points in time can be calculated by multiplying or dividing by 1.05, raised to the appropriate power.

 Value as of time 0 = \$1 [(1.053 – 1) / 0.05] / 1.052 = \$2.8594 Value as of time 4 = \$1 [(1.053 – 1) / 0.05] 1.052 = \$3.4756

The standard present value annuity formula gives a value one period before the first payment of the annuity. Therefore, the formula will give you a value at t = -1. You need to multiply by 1 + r to get the value by t = 0.

 Value as of time 0 = \$1 { [1 – (1/1.05)3] / (0.05) } 1.051 = \$2.8594

The values at time 2 and 4:

 Value as of time 2 = \$1 { [1 – (1/1.05)3] / (0.05) } 1.053 = \$3.1525 Value as of time 4 = \$1 { [1 – (1/1.05)3] / (0.05) } 1.055 = \$3.4756

1. Five-year annuity of \$1 per year, first cash flow received at t = 3. Interest and discount rate = 5%.

 0 1 2 3 4 5 6 7 8 \$0 \$0 \$0 \$1 \$1 \$1 \$1 \$1 \$0

The standard future value annuity formula gives the value as of the last year of the annuity (t = 7 in this example). This is a five-year annuity. Therefore, 1.05 is raised to the fifth power.

 Value as of time 7 = \$1 [(1.055 – 1) / 0.05] = \$5.5256

Values at different points in time using the future value annuity formula. A couple of examples

 Value as of time 0 = \$1 [(1.055 – 1) / 0.05] / 1.057 = \$3.9270 Value as of time 4 = \$1 [(1.055 – 1) / 0.05] / 1.053 = \$4.7732 Value as of time 8 = \$1 [(1.055 – 1) / 0.05] 1.051 = \$5.8019

The standard present value annuity formula gives the value as of the year before the first payment of the annuity (t = 2 in this example).

 Value as of time 2 = \$1 { [1 – (1/1.05)5] / (0.05) } = \$4.3295

Values at different points in time using the present value annuity formula. A couple of examples:

 Value as of time 0 = \$1 { [1 – (1/1.05)5] / (0.05) } / 1.052 = \$3.9270 Value as of time 4 = \$1 { [1 – (1/1.05)5] / (0.05) } 1.052 = \$4.7732 Value as of time 8 = \$1 { [1 – (1/1.05)5] / (0.05) } 1.056 = \$5.8019

1. Growing Finite Annuities

1. Four-year growing annuity, growing at 10% per year. First cash flow (equal to \$1) received at t = 1. Interest and discount rate = 5%.

 0 1 2 3 4 5 \$0 \$1 \$1.1 \$1.21 \$1.331 \$0

Standard formula for the present value of a finite growing annuity (for when r is not equal to g) =

Cfirst [1 – [(1 + g) / (1 + r)]t ] / (r – g). This formula gives the value one period before the first payment (t = 0 in this example).
Cfirst is the first cash flow of the annuity. In this above example, Cfirst = C1 = \$1.

 Value as of time 0 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } \$4.0904

Values at different points in time using the present value growing annuity formula. Multiply or divide by 1+r (raised to the appropriate power) to determine the value at other points in time.

 Value as of time 2 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } 1.052 \$4.5096 Value as of time 4 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } 1.054 \$4.9719 Value as of time 5 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } 1.055 \$5.2205

1. Four-year growing annuity, growing at 10% per year. First cash flow (equal to \$1) received at t = 3. Interest and discount rate = 5%.

 0 1 2 3 4 5 6 7 \$0 \$0 \$0 \$1 \$1.1 \$1.21 \$1.331 \$0

The standard formula for the present value of a growing annuity gives you a value at time 2 (one period before the first payment). This is a 4-year annuity. Therefore, 1.05 is raised to the 4th power.

 Value as of time 2 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } \$4.0904

Values at different points in time using the present value growing annuity formula. A few examples:

 Value as of time 0 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } /1.052 \$3.7101 Value as of time 5 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } 1.053 \$4.7351

1. Perpetual constant annuities

1. Perpetual constant annuity of \$1 (cash flows start at time 1, interest and discount rate = 5%)

 0 1 2 3 4 5  \$0 \$1 \$1 \$1 \$1 \$1 \$1

The standard formula for the present value of a perpetual constant annuity is C / r. The formula gives you the value one period before the first payment.

 Value as of time 0 = \$1 / 0.05 \$20.0000

Values at different points in time using the present value perpetual constant annuity formula

 Value as of time 1 = (\$1 / 0.05) 1.051 \$21.0000 Value as of time 4 = (\$1 / 0.05) 1.054 \$24.3101

1. Perpetual constant annuity of \$1 (cash flows start at time 0, interest and discount rate = 5%)

 0 1 2 3 4 5  \$1 \$1 \$1 \$1 \$1 \$1 \$1

The standard formula for the present value of a perpetual constant annuity gives you the value one period before the first payment (t = -1 in this example). Therefore, you need to multiply by 1.05 to get the value at t = 0.

 Value as of time 0 = (\$1 / 0.05) 1.05 \$21.0000

Values at different points in time using the present value perpetual annuity formula. Two examples:

 Value as of time 1 = (\$1 / 0.05) 1.052 \$22.0500 Value as of time 4 = (\$1 / 0.05) 1.055 \$25.5256

1. Perpetual constant annuity of \$1 (cash flows start at time 5, interest and discount rate = 5%)

 0 1 2 3 4 5  \$0 \$0 \$0 \$0 \$0 \$1 \$1

The standard formula for the present value of a perpetual constant annuity gives you the value one period before the first payment (t = 4 in this example).

 Value as of time 4 = (\$1 / 0.05) \$20.0000

Values at different points in time using the present value perpetual annuity formula. Some examples:

 Value as of time 0 = (\$1 / 0.05) / 1.054 \$16.4540 Value as of time 5 = (\$1 / 0.05) 1.051 \$21.0000

1. Perpetual growing annuity, growing at 3% per year (first cash flow, received at time 1, equals \$1, interest and discount rate = 5%)

 0 1 2 3  \$0 \$1 \$1.03 \$1.0609 3% more

The standard formula for the present value of a perpetual growing annuity is Cfirst / (r – g). The formula gives you the value one period before the first payment.

 Value as of time 0 = \$1 / (0.05 – 0.03) \$50.0000

Values at different points in time using the present value perpetual growing annuity formula. Some examples:

 Value as of time 1 = [\$1 / (0.05 – 0.03)] 1.051 \$52.5000 Value as of time 4 = [\$1 / (0.05 – 0.03)] 1.054 \$60.7753

1. Perpetual growing annuity, growing at 3% per year (first cash flow, received at time 11, equals \$1, interest discount rate = 5%)

 10 11 12 13  \$0 \$1 \$1.03 \$1.0609 3% more

The standard formula for the present value of a perpetual growing annuity gives you the value one period before the first payment (t = 10 in this example).

 Value as of time 10 = [\$1 / (0.05 – 0.03)] \$50.0000

Values at different points in time using the present value perpetual growing annuity formula. A few examples:

 Value as of time 0 = [\$1 / (0.05 – 0.03)] / 1.0510 \$30.6957 Value as of time 9 = [\$1 / (0.05 – 0.03)] / 1.051 \$47.6190 Value as of time 11 = [\$1 / (0.05 – 0.03)] 1.051 \$52.5000

1. Two growth-rate example: \$1 at time 1, 10% growth rate until time 4, 3% growth rate after time 4 (in perpetuity). Use a 5% discount rate

 0 1 2 3 4 5  \$0 \$1 \$1.1 \$1.21 \$1.331 \$1.3709 3% more

Value the first four payments using the finite growing annuity formula. Value the payments starting at time 5 using the perpetual growing annuity formula

The first four payments

 Value as of time 0 = \$1 { [1 – (1.10/1.05)4] / (0.05 – 0.10) } \$4.0904

The payments starting at time 5

 Value as of time 0 = {[(\$1) (1.13) (1.03)] / [(0.05 – 0.03)]} / 1.054 \$56.3934

Solution = \$4.0904 + \$56.3934 = \$60.4837

Note: [(\$1) (1.13) (1.03)] = \$1.3709 = the payment at t = 5

1. Two growth-rate example: \$1 at time 0, 10% growth rate until time 12, 3% growth rate after time 12 (in perpetuity). Use a 5% discount rate

 0 1 2 . . . 11 12 13  \$1 \$1.1 \$1.21  \$2.8531 \$3.1384 \$3.2326 3% more

Value the first thirteen payments (t = 0 to t = 12) using the finite growing annuity formula. Value the payments starting at time 13 using the perpetual growing annuity formula

The first thirteen payments

 Value as of time 0 = \$1 { [1 – (1.10/1.05)13] / (0.05 – 0.10) } 1.051 \$17.4471

The payments starting at time 13

 Value as of time 0 = {[(\$1) (1.112) (1.03)] / [(0.05 – 0.03)]} / 1.0512 \$90.0011

Solution = \$17.4471 + \$90.0011 = \$107.4482

Note: [(\$1) (1.112) (1.03)] = \$3.2326 = the payment at t = 13

1. Two growth-rate example: \$1 at time 3, 10% growth rate until time 20, 3% growth rate after time 20 (in perpetuity). Use a 5% discount rate

 0 1 2 3 4 . . . 20 21  \$0 \$0 \$0 \$1 \$1.1  \$5.0545 \$5.2061 3% more

Value the first eighteen payments (t = 3 to t = 20) using the finite growing annuity formula. Value the payments starting at time 21 using the perpetual growing annuity formula

The first eighteen payments

 Value as of time 0 = \$1 { [1 – (1.10/1.05)18] / (0.05 – 0.10) } / 1.052 \$23.7689

The payments starting at time 21

 Value as of time 0 = {[(\$1) (1.117) (1.03)] / [(0.05 – 0.03)]} / 1.0520 \$98.1063

Solution = \$23.7689 + \$98.1063 = \$121.8752

Note: [(\$1) (1.117) (1.03)] = \$5.2061 = the payment at t = 21

1. Internal rate of return (IRR)

Definition: the IRR = the discount rate that causes the sum of the present values of all cash flows to equal zero.

IRR calculation examples

1. Two cash flows

 0 1 2 3 4 5 -\$1 \$0 \$0 \$0 \$0 \$2

-\$1 + \$2 / (1 + r)5 = \$0

r = (\$2 / \$1)(1/5) – 1 = 14.8698% = IRR

Financial Calculator: N = 5, I/Y = Answer, PV = -1, PMT = 0, FV = 2

 0 1 2 3 4 5 \$1 \$0 \$0 \$0 \$0 -\$2

\$1 + -\$2 / (1 + r)5 = \$0

r = (\$2 / \$1)(1/5) – 1 = 14.8698% = IRR

Financial Calculator: N = 5, I/Y = Answer, PV = 1, PMT = 0, FV = -2

1. Perpetual constant annuities

 0 1 2 3 4  -\$10 \$1 \$1 \$1 \$1 \$1

-\$10 + \$1 / r = \$0

r = \$1 / \$10 = 10% = IRR

1. Perpetual growing annuities

 0 1 2 3 4  -\$10 \$1 \$1.03 \$1.0609 \$1.0927 3% more

-\$10 + \$1 / (r – 3%) = \$0

r = (\$1 / \$10) + 3% = 13% = IRR

1. Other cash flow patterns – solve by your calculator or computer. Example – finite annuity

 0 1 2 3 4 5 -\$3 \$1 \$1 \$1 \$1 \$1

-\$3 + \$1 { [1 – (1/(1+r))5] / r } = \$0

r = 19.8577% = IRR

Financial Calculator: N = 5, I/Y = Answer, PV = -3, PMT = 1, FV = 0

1. Modified Internal Rate of Return (MIRR)

• Step one: Using the discount rate, take a PV (to time zero) of the negative cash flows

• Step two: Using the interest rate, take a FV (to time t, where t is the time of the last cash flow) of the positive cash flows

• Step three: Calculate the IRR of the two cash flows calculated in the first two steps

1. Using an interest and discount rate = 5%, what is the MIRR of the following cash flow stream?

 0 1 2 3 4 5 -\$3 \$1 \$1 \$1 \$1 \$1

Step 1: PV of negative cash flows (at time 0) = -\$3

Step 2: FV of positive cash flows (at time 5) = \$5.5256

Step 3: IRR = (\$5.5256 / \$3)(1/5) – 1 = 12.9932% = MIRR

1. Using an interest and discount rate = 5%, what is the MIRR of the following cash flow stream?

 0 1 2 3 4 5 +\$3 -\$1 -\$1 -\$1 -\$1 -\$1

Step 1: PV of negative cash flows (at time 0) = -\$4.3295

Step 2: FV of positive cash flows (at time 5) = \$3.8288

Step 3: IRR = (\$3.8288 / \$4.3295)(1/5) – 1 = -2.4277% = MIRR

1. Using an interest and discount rate = 5%, what is the MIRR of the following cash flow stream?

 0 1 2 3 4 5 +\$3 \$0 \$0 -\$1 -\$1 \$1

Step 1: PV of negative cash flows (at time 0) = -\$1.6865

Step 2: FV of positive cash flows (at time 5) = \$4.8288

Step 3: IRR = (\$4.8288 / \$1.6865)(1/5) – 1 = 23.4154% = MIRR

1. Application – loan amortization schedules

A 30-year home loan has an annual interest rate of 8%. Interest is compounded monthly. What is the monthly payment on a fully amortizing, level payment loan for \$100,000? \$733.7646

Use this payment to filling in the following loan amortization table for the home loan described above.

 Month Beginning Balance Total Payment Interest Payment Principal Payment Ending Balance 0 \$100,000.000 1 \$100,000.000 \$733.7646 \$666.6667 \$67.0979 \$99,932.9021 2 \$99,932.9021 \$733.7646 \$666.2193 \$67.5452 \$99,865.3569 3 \$99,865.3569 \$733.7646 \$665.7690 \$67.9955 \$99,797.3613 4 \$99,797.3613 \$733.7646 \$665.3157 \$68.4488 \$99,728.9125 5 \$99,728.9125 \$733.7646 \$664.8594 \$68.9052 \$99,660.0073

The loan balance will be \$0 after the 360th payment.

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