Question

Amount invested today					238,000
Annual rate of return					8.3%
Years until maturity					21
You are thinking about retirement, and would like
to compute how much you will have some time in
the future.
Using the data from above, please compute future
amounts, and then answer these questions:
#1 How much MORE will you have if compounding is
monthly rather than annually?

#2 How much MORE will you have if compounding is
daily rather than monthly?
A Between 4,000 and 10,000
B Between 10,000 and 12,000
C Between 12,000 and 14,000
D Between 14,000 and 20,000

Answer 1

For annual compounding:

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=238,000*(1.083)^21

=238,000*5.335776

=$1269914.69(Approx)

1.For monthly compounding:

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=238,000*(1+0.083/12)^(12*21)

=238,000*5.68027574

=$1351905.63(Approx)

Hence excess value=1351905.63-1269914.69

=$81990.94(Approx)

2.

For daily compounding:

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=238,000*(1+0.083/365)^(365*21)

=238,000*5.71332893

=$1359772.29(Approx)

Hence excess value=1359772.29-1351905.63

=$7866.66(Approx)

Hence the correct option is:

Between 4,000 and 10,000