﻿ Amortization ## Amortization Examples

### Example 1 - Find the Present Value

How much could you borrow if you could afford to make payments of \$150 at the end of each month for 4 years at 5% compounded monthly? How much interest would you pay?

`i = r/ppy = .05/12 = 0.00416666...`

Since the periodic rate is a repeating decimal, we will calculate it as part of the future value calculation. We do not simply round this value off and use it. That would lead to inaccurate results.

`n = t * ppy = 4 * 12 = 48`
`PV = PMT[1 - (1+i)-n]/i = 150[1 - (1 + 0.05/12)-48]/(0.05/12)= \$6,513.44` 150  1  1 .05 12   48   0.05 12  6513.443

The interest is the difference between what you got out and what you put in (keeping in mind that you got less than you put in):

`I =  n*PMT - PV = 48 * 150 - 6,513.44 = \$686.56`

Using the TI-83 TVM Solver

Set the TVM variables as follows:

```N=48
I%=5
PV=?
PMT=-150 (representing cash outflow)
FV=0
P/Y=12
C/Y=12
PMT:END```

Move the cursor to the PV variable and press  .

### Example 2 - Find Periodic Payment

How much would you have to pay at the end of each quarter if you borrowed \$20,000 for 10 years at 5.2% compounded quarterly?

`i = r/ppy = 0.052/4 = 0.013`
`n = t * ppy = 10 * 4 = 40`
`PMT = PV*i/[1-(1+i)-n] = 20000*0.013/(1 - 1.013-40) = \$644.39` 20000 0.013  1 1.013  40  644.3875802

Using the TI-83 TVM Solver

Set the TVM variables as follows:

```N=40
I%=5.2
PV=-20000
PMT=?
FV=0
P/Y=4
C/Y=4
PMT:END```

Move the cursor to the PMT variable and press  .