Question

4.5 Calculating the Number of Periods Solve for the unknown number of years in each of the following:

Present Value                   Years                    Interest Rate                     Future Value

$ 625                                                                 7%                                       $ 1,104

810                                                                    12                                        5,275

16,500                                                              17                                        245,830

21,500                                                              8                                           215,000

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

a.

1104=625*(1.07)^n

(1104/625)=(1.07)^n

Taking log on both sides;

log (1104/625)=n*log 1.07

n=log (1104/625)/log 1.07

=8.41 years(Approx).

b.

5275=810*(1.12)^n

(5275/810)=(1.12)^n

Taking log on both sides;

log (5275/810)=n*log 1.12

n=log (5275/810)/log 1.12

=16.53 years(Approx).

c.

245830=16500*(1.17)^n

(245830/16500)=(1.17)^n

Taking log on both sides;

log (245830/16500)=n*log 1.17

n=log (245830/16500)/log 1.17

=17.21 years(Approx).

d.

215,000=21500*(1.08)^n

(215,000/21500)=(1.08)^n

Taking log on both sides;

log (215,000/21500)=n*log 1.08

n=log (215,000/21500)/log 1.08

=29.92 years(Approx).