Question

What is the difference in future value if $40,000 is invested at 5% over twenty years, with one option compounding interest annually, while the other is based on monthly compounding?

Answer 1

Ans:

Step 1: Future value compounded annually.

Formula to compute future value of sum invested at a rate of r for t number of years compounded n times,

FV = PV * (1+r/n)nt

FV = Future value = ?

PV = Present value = $ 40,000.

r = rate of interest = 5%

t = number of years = 20 years.

n = number of time compounded per year = 1

Insert above data in the formula

FV = PV * (1+r/n)nt

FV = $ 40,000 * (1+5%)20*1

FV = $ 40,000 * (1.05)20

FV = $ 106,131.91

Step 2 :

Future value compounded monthly.

Formula to compute future value of sum invested at a rate of r for t number of years compounded n times,

FV = PV * (1+r/n)nt

FV = Future value = ?

PV = Present value = $ 40,000.

r = rate of interest = 5%

t = number of years = 20 years.

n = number of times compounded per year = 12

Insert above data in the formula

FV = PV * (1+r/n)nt

FV = $ 40,000 * (1+(5%/12))20*12

FV = $ 40,000 * (1.004167)240

FV = $ 40,000* 2.712856

FV = $ 108,514.3

Step 3: Difference between future value of step 1 and step 2

Difference = $ 108,514.3 - $ 106,131.91

= $ 2,382.39