Question

Anthony and Michelle Constantino just got married and received $20,000 in cash gifts for their wedding. How much will they have on their​ twenty-fifth anniversary if they place half of this money in a​ fixed-rate investment earning 10 percent compounded​ annually? Would the future value be larger or smaller if the compounding period was 6​ months? How much more or less would they have earned with this shorter compounding​ period?

Answer 1

The following information is given in the question:

Gift value	$ 20,000
Invested amount	$ 10,000
Tenure in years	25
Rate of return	10%

The formula for Future Value is FV = PV*(1+i)^n where, FV = Future Value, PV = Present Value , i = Interest Rate, n = number of compounding periods

Scenario 1: Interest rate is compounded annually i.e. once a year.

If we solve the formula using the information given in the question and take the compounding frequency as annual, the working would be as follows:

FV = 10000*(1+10%)^25

FV = 10000*(1+0.1)^25

FV = 10000*(1.1)^25

FV = 10000*(10.8347059433884)

FV = 108,347.06

Thus, if interest is compounded annually, Anthony and Michelle Constantino would have $ 108,347.06 on their 25th anniversary.

Scenario 2: Interest rate is compounded half-yearly i.e. twice a year.

If we solve the formula using the information given in the question and take the compounding frequency as half-yearly, the working would be as follows:

FV = 10000*(1+10%)^(25*2)

FV = 10000*(1+0.1)^50

FV = 10000*(1.1)^50

FV = 10000*(117.390852879696)

FV = 1,173,908.53

Thus, if interest is compounded half-yearly, Anthony and Michelle Constantino would have $ 1,173,908.53 on their 25th anniversary.

With the shorter compounding period, they would have received an additional amount of $ 1,065,561.47. This figure is obtained as the difference between the future value amounts calculated in both the scenarios above.

The future value amount in Scenario 2 is significantly higher than that in Scenario 1 is because of the shorter compounding period. A shorter compounding period means that interest is calculated more often and that too on the accumulated balance i.e. principal + interest.

Note: The amount on hand at the end of 25 years is only the investment proceeds and does not include $ 10,000 that was retained as cash.