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

1501.05124810.0512**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 .

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

200000.0131.013401**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 .