Question

Joshua invested $750 in an account paying an interest rate of

3 1/4% compounded quarterly. Josiah invested $750 in an account paying an interest rate of 2 5/8 % compounded annually. After 18 years, how much more money would Joshua have in his account than Josiah, to the nearest dollar?

Answer 1

Due to the difference in the interest rate and the quarterly compounding, Joshua will have $212.24 more than Josiah.
Explanation:
Giving the following information:
Joshua:
Initial investment (PV)= $750
Interest rate (i)= 0.0341/4= 0.008525
Number of periods (n)= 18*4= 72 quarters
Josiah:
Initial investment (PV)= $750
Interest rate (i)= 0.0285
Number of periods (n)= 18 years
To calculate the future value of each one, we need to use the following formula:
FV= PV*(1 + i)^n
Joshua:
FV= 750*(1.008525^72)
FV= $1,381.98
Josiah:
FV= 750*(1.0285^18)
FV= $1,169.74
Due to the difference in the interest rate and the quarterly compounding, Joshua will have $212.24 more than Josiah.