You plan to invest $2,000 annually. The first $2,000 will be invested on your 22^nd birthday and the last $2,000 will be invested on your 49^th birthday. What is the value of this investment on your 50^th birthday if all invested funds earn 8% annually?

Question

Quizplus · Accepted Answer

Using the formula for the future value of an annuity, we can calculate the value of the investment on the 50th birthday:
FV = PMT x [(1+r)^n - 1]/r
where PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

In this case, PMT = $2,000, r = 8%, and n = 29 (the number of years between the 22nd and 49th birthdays, inclusive). Note that we need to use the formula with the payment at the end of each period, since the last payment is made on the 49th birthday.

FV = $2,000 x [(1+0.08)^29 - 1]/0.08 = $205,931.87

Therefore, the investment will be worth $205,931.87 on the 50th birthday. The correct answer is (A).

You Plan to Invest $2,000 Annually