Question

How long will it take $400 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.

A.5%

B.12%

C.19%

D.100%

Answer 1

We use the formula:

A=P(1+r/100)^n

where

A=future value($800)

P=present value($400)

r=rate of interest

n=time period.

a.

800=400(1.05)^n

(800/400)=1.05^n

Taking log on both sides;

log 2=n*log 1.05

Hence n=log 2/log 1.05

which is equal to

=14.21 years(Approx).

b.

(800/400)=1.12^n

Taking log on both sides;

log 2=n*log 1.12

Hence n=log 2/log 1.12

which is equal to

=6.12 years(Approx).

c.

(800/400)=1.19^n

Taking log on both sides;

log 2=n*log 1.19

Hence n=log 2/log 1.19

which is equal to

=3.98 years(Approx).

d.

(800/400)=2^n

Taking log on both sides;

log 2=n*log 2

Hence n=log 2/log 2

which is equal to

=1 year.