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
480.0512
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
.
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
200000.01311.01340
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
.