Question

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.):

Present Value	Years	Interest Rate	Future Value
$570		8%	$1,293
820		12	2173
18500		18	343880
21600		14	363176

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.

1.

1293=570*(1.08)^n

(1293/570)=(1.08)^n

Taking log on both sides;

log (1293/570)=n*log 1.08

n=log (1293/570)/log 1.08

=10.64 years(Approx).

2.

2173=820*(1.12)^n

(2173/820)=(1.12)^n

Taking log on both sides;

log (2173/820)=n*log 1.12

n=log (2173/820))/log 1.12

=8.60 years(Approx).

3.

343880=18500*(1.18)^n

(343880/18500)=(1.18)^n

Taking log on both sides;

log (343880/18500)=n*log 1.18

n=log (343880/18500)/log 1.18

=17.66 years(Approx).

4.

363176=21600*(1.14)^n

(363176/21600)=(1.14)^n

Taking log on both sides;

log (363176/21600)=n*log 1.14

n=log (363176/21600)/log 1.14

=21.54 years(Approx).