Question

Solve for the unknown number of years in each of the following:

Present Value	Years	Interest Rate(%)	Future Value
500		8	1,075
750		12	1,836
17800		18	294,671
20900		14	320,610

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.1075=500*(1.08)^n

(1075/500)=(1.08)^n

Taking log on both sides;

log (1075/500)=n*log 1.08

n=log (1075/500)/log 1.08

=9.95 years(Approx)

b.1836=750*(1.12)^n

(1836/750)=(1.12)^n

Taking log on both sides;

log (1836/750)=n*log 1.12

n=log (1836/750)/log 1.12

=7.9 years(Approx)

c.294671=17800*(1.18)^n

(294671/17800)=(1.18)^n

Taking log on both sides;

log (294671/17800)=n*log 1.18

n=log (294671/17800)/log 1.18

=16.96 years(Approx)

d.320610=20900*(1.14)^n

(320610/20900)=(1.14)^n

Taking log on both sides;

log (320610/20900)=n*log 1.14

n=log (320610/20900)/log 1.14

=20.84 years(Approx)