It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account).Darwin will put $1000 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 Darwin have in his account at the end of the 40th year? Assume that the account pays 12% interest compounded annually and round to nearest $1000.
A) $93,000
B) $766,000
C) $767,000
D) $850,000

Question

Quizplus · Accepted Answer

To solve this problem we will use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

where:
P = the annual payment
r = the interest rate per period (in this case, per year)
n = the number of periods (in this case, 40 years)

In this problem, P = $1000, r = 12%, and n = 40. Plugging these values into the formula, we get:

FV = $1000 * ((1 + 0.12)^40 - 1) / 0.12
   = $767,041.47

Rounding this to the nearest $1000 gives us the final answer of $767,000, which corresponds to choice C.

It Is January 1st and Darwin Davis Has Just Established