Question

You are saving to buy a $175,000 house. There are two competing banks in your area, both offering certificates of deposit yielding 6 percent.

Requirement 1:

How long will it take your initial $92,000 investment to reach the desired level at First Bank, which pays simple interest? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Number of years

Requirement 2:

How long will it take your initial $92,000 investment to reach the desired level at Second Bank, which compounds interest monthly? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Number of years

Answer 1

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

=92000*6%*Time period

=5520*Time period

Future value=Principal+Simple interest

175,000=92000+5520*Time period

Time period=(175,000-92000)/5520

=15.04 years(Approx)

b.We use the formula:
A=P(1+r/12)^12n
where
A=future value
P=present value  
r=rate of interest
n=time period.

175,000=92000*(1+0.06/12)^(12n)

(175,000/92000)=(1.005)^(12n)

Taking log on both sides;

log (175,000/92000)=12n*log 1.005

n=1/12[log (175,000/92000)/log 1.005]

=10.74 years(Approx)