Question

Calculate the future value of $2000 invested at 5% annual simple interest rate over a period of 5 years

5% annual interest rate compounded yearly over a period of 5 years where the is no withdrawal from the account

5% annual interest rate compounded semiannually over a period of 5 years when there is no withdrawal from the account.

When we gain more? Explain why?

Answer 1

Future value using simple interest = Principal ( 1 + rate * time)

Future value = 2000 ( 1 + 0.05 * 5)

Future value = 2000 * 1.25

Future value = $2,500

Future value using compound interest = Present value ( 1 + r)ⁿ

Future value = 2000 ( 1 + 0.05)⁵

Future value = 2000 * 1.276282

Future value = $2,552.563

When compounded semi annually:

Rate = 0.05 / 2 = 0.025

Number of periods = 5 * 2 = 10

Future value = 2000 ( 1 + 0.025)¹⁰

Future value = 2000 * 1.280085

Future value = $2,560.1691

We gain more when the interest rate is compounded semi annually.

Interest compounding refers to the impact of added accrued interest throughout the term of the investment. For example, if interest is compounded semi-annually, that means every 6 months little more interest is added to the balance of the account, increasing the amount of interest the account accrues. If interest is compounded annually, the interest that accrues on day one doesn’t start earning additional interest until a year later.