It is January 1st and Jeff Davis has just established a Superannuation account.Jeff will put $1,000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total).How much money will Jeff have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually,and round to the nearest $1,000.
A)$93,000
B)$766,000
C)$767,000
D)$850,000

Question

Quizplus · Accepted Answer

This is a case of a regular annuity since Jeff will be depositing the same amount at the end of every year. Using the formula for regular annuities, we have:
PMT = $1,000
r = 12% = 0.12
n = 40 (number of years)
Using the formula for future value of a regular annuity, we have:
FV = PMT * ((1 + r)^n - 1) / r
FV = $1,000 * ((1 + 0.12)^40 - 1) / 0.12
FV = $766,470.74
Rounding to the nearest $1,000, Jeff will have $767,000 in his account at the beginning of the 41st year. Therefore, the answer is C.

It Is January 1st and Jeff Davis Has Just Established