find future value and interest

Question

Find the future value and interest earned if $480.00 is invested at 8% compounded
(a) quarterly for 3 years.
(b) continuously for 3 years.

Answer 1

Hello, thank you for taking the time to post your question!

For compounded quarterly you want to use the formula

FV = P(1 + r/n)^(nt) …. For the values on this question that becomes

FV = 480(1 + 0.08/4)^(4*3)

FV = 480(1.02)^12

FV = 608.76

So the future value there is $608.76 and the interest earned is 608.76 – 480 = $128.76

Then for the other part of the question where it’s the same length of time but now interest is compounded continuously you want to update the formula to be

FV = P*e^(rt)

FV = 480 * e^(0.08*3)

FV = 480 * e^(0.24) = 610.20

So you end up with slightly higher values of the future value being $610.20 and the interest earned being 610.20 – 480 = $130.20

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

 a)

      480( 1 + 0.08/4)¹² = 608. 76

 

 

b)  480( 1 + 0.08) ³ = 604.66