Question

6. How long will it take for $1 to double in value (disregarding any change in the buying power of the dollar) if:

a) The interest rate is 10% compounded annually? b) The interest rate is 10% compounded semiannually? c) The interest rate is 10% ordinary simple interest?

Answer 1

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

(2*1)=1*(1.1)^n

2=(1.1)^n

Taking log on both sides;

log 2=n*log (1.1)

n=log 2/log (1.1)

=7.27 years(Approx)

b.We use the formula:  
A=P(1+r/2)^2n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

(2*1)=1*(1+0.1/2)^(2n)

2=(1.05)^2n

Taking log on both sides;

log 2=2n*log 1.05

n=1/2[log 2/log 1.05]

=7.10 years(Approx)

c.Simple interest=Principal*Interest rate*Time period

=1*0.1*Time period

=0.1*Time period

Future value=Principal+Simple interest

2=1+(0.1*Time period)

Time period=(2-1)/0.1

=10 years