Interest rate

Question

You have won a lottery and have $25,000 to invest. After visiting several savings institutions you realize that you need to choose between an account that offers an interest rate of 3.75% compounded annually and another account that offers 3.52% compounded continuously. Compare the amount of money you expect to receive from each option after 10 years. Which option would you choose? Why?

Answer 1

"an interest rate of 3.75% compounded annually" uses the formula Future value = Principal x (1 + r)^t, where r = annual rate, and t = time

 

In this case, we get FV = $25,000 x (1.0375)¹⁰, which is $25,000 x 1.445 = $36,125

 

"3.52% compounded continuously" uses a different formula, which is Future Value =  Pe^rt

where r = rate, t = time, and e is a constant with a value of 2.7183

First, we multiply 0.0352 by 10 to get the exponent for our formula = 0.352

So, $25,000 x 2.7183^0.352 = $25,000 x 1.4437 ≅ $36,092

 

We conclude that, due to the higher interest rate, the investment at 3.75% will yield slightly more money.