Question

Consider a deposit of $100,000 that can be made into one of four banks. Which of the following provides the largest balance by the end of five years?

A. Bank A: 5.0% compounded daily

B. Bank B: 5.2% compounded monthly

C. Bank C: 6.0% simple interest

D. Bank D: 5.4% compounded annually

Answer 1

a.We use the formula:
A=P(1+r/365)^365n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=100,000*(1+0.05/365)^(365*5)

=100,000*1.28400343

=$128400.34(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.

A=100,000*(1+0.052/12)^(12*5)

=100,000*1.29620179

=$129620.18(Approx).

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

=100,000*6%*5=$30000

Future value=Principal+Simple interest

=100,000+30000=$130,000

d.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=100,000*(1.054)^5

=100,000*1.30077761

=$130077.76(Approx)

Hence largest balance would be for:

D. Bank D: 5.4% compounded annually