Question

Calculating the Number of Periods (LO4) each of the following Solve for the unknown number of years in Present Value Years Interest Rate Future Value $1,389 $560 810 1,821 10 18,400 17 289,715 21,500 15 430,258

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.

1389=560*(1.09)^n

(1389/560)=(1.09)^n

Taking log on both sides;

log (1389/560)=n*log 1.09

n=log (1389/560)/log 1.09

=10.54 years(Approx).

b.

1821=810*(1.1)^n

(1821/810)=(1.1)^n

Taking log on both sides;

log (1821/810)=n*log 1.1

n=log (1821/810)/log 1.1

=8.5 years(Approx).

c.

289,715=18400*(1.17)^n

(289,715/18400)=(1.17)^n

Taking log on both sides;

log (289,715/18400)=n*log 1.17

n=log (289,715/18400)/log 1.17

=17.56 years(Approx).

d.

430,258=21500*(1.15)^n

(430,258/21500)=(1.15)^n

Taking log on both sides;

log (430,258/21500)=n*log 1.15

n=log (430,258/21500)/log 1.15

=21.44 years(Approx).