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 40^th 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

Using the formula for compound interest:

A = P(1 + r)^n
where:
A = final amount
P = principal (initial amount)
r = annual interest rate
n = number of years

We can solve for the final amount in Darwin's IRA:

A = 1000(1 + 0.12)^40 + 1000(1 + 0.12)^39 + ... + 1000(1 + 0.12)^1

Using a financial calculator or spreadsheet, this simplifies to approximately $767,000. Rounded to the nearest thousand, the answer is choice C.

It Is January 1st and Darwin Davis Has Just Established