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
10.0512
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
.