anice plans to save $75 a month, starting today, for 20 years. Kate plans to save $80 a month for 20 years, starting one month from today. Both Janice and Kate expect to earn an average return of 5.5 percent on their savings. At the end of the 20 years, how much more Kate willhave than Janice

Kate will have $2,178 more than Janice

Explanation:

The constant saving of $75 and $80 each month is an annuity payment. The Balance at the end of 20 years of a constant payment is the future value of annuity.

n = number of months = 20 x 12 = 240 months

r = Average rate = 5.5% per year = 5.5% / 12 = 0.46%

Future value of annuity = FV = P x ([ 1 + r ]^n - 1) / r

Janice

Saving per month = $75

FV = $75 x ([ 1 + 5.5%/12 ]^240 - 1) / 5.5%/12 = $32,672

Kate

Saving per month = $80

FV = $80 x ([ 1 + 5.5%/12 ]^240 - 1) / 5.5%/12 = 34,850.2

Difference = $34850.2 - 32,672 = $2,178