﻿ Sinking Fund ## Sinking Fund Examples

### Example 1 - Find Future Value

If you invest \$150 at the end of each month for 4 years at 5% compounded monthly, how much will be in the account at the end of the 4 years and how much interest will you have earned?

`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`
`FV = PMT[(1+i)n - 1]/i = 150[(1 + 0.05/12)48 - 1]/(0.05/12)= \$7,952.23` 150   1 .05 12  48 1   0.05 12  7952.232781

The interest is the difference between what you got back and what you invested:

I = A - n*PMT = 7,952.23 - 48 * 150 = \$752.23

Using the TI-83 TVM Solver

Set the TVM variables as follows:

```N=48
I%=5
PV=0
PMT=150
P/Y=12
C/Y=12
PMT:END```

Move the cursor to the FV variable and press  .

### Example 2 - Find Periodic Payment

How much would you have to invest at the end of each quarter if you wanted to have \$20,000 at the end of 10 years. Assume that the account pays 5.2% compounded quarterly.

`i = r/ppy = 0.052/4 = 0.013`
`n = t * ppy = 10 * 4 = 40`
`PMT = FV*i/[(1+i)n - 1] = 20000*0.013/(1.013)40 -1) = \$384.39` 20000 0.013  1.013 40 1  384.39

Using the TI-83 TVM Solver

Set the TVM variables as follows:

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

Move the cursor to the PMT variable and press  .