Question

You currently have $5,700. First United Bank will pay you an annual interest rate of 9.2, while Second National Bank will pay you an annual interest rate of 10.3. How many fewer years must you wait for your account value to grow to $16,600 at Second National Bank?

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.

First United Bank:

16600=5700*(1.092)^n

(16600/5700)=(1.092)^n

Taking log on both sides;

log (16600/5700)=n*log 1.092

n=log (16600/5700)/log 1.092

=12.15 years(Approx).

Second National  Bank:

16600=5700*(1.103)^n

(16600/5700)=(1.103)^n

Taking log on both sides;

log (16600/5700)=n*log 1.103

n=log (16600/5700)/log 1.103

=10.90 years(Approx)

Hence fewer years to wait=(12.15-10.90) years

=1.25 years(Approx).