Question

Checked		Compoundin g
Test 21
Amount invested today					209,000
Annual rate of return					8.8%
Years until maturity					24
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?					(not graded)
Please answer the following question:
#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

Compound Interest formula:

Where,
A = Amount at maturity
P = Present value of investment
i = rate of interest
n = number of periods

When it is compounded annully.
Given:

P = 209,000
i = 8.8% or 0.088
n = 24

Substituting the values in the formula, we get:

When it is compounded monthly, there will be a small modification in formula:

Where,
a = number of compounding per year.

when it is compounded monthly , a = 12

Using the same values above in the formula, we get

When compounding daily, a = 365

Therefore, substituting the values in the formula, we get:

Now we can answer the questions:

When compounded annually A = $1,582,121.29
When compounded monthly A =  $1,714,073.37
When compounded daily A = $1,726,894.00

#1. We will have  $131,952.08 more if it is compounded monthly rather than annually ($1,714,073.37 - . $1,582,121.29)

#2. We will have  $12,820.63 more if it is compounded daily rather than monthly ($1,726,894.00 - $1,714,073.37).
Option C is correct.