Bram Johnson invests $500 at the end of each quarter for 10 years. The account earns 12% interest annually. What is the value of the account at the end of 10 years?

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity to find the value of the account:

FV = PMT x [((1 + r/n)^(n*t) - 1) / (r/n)]

where:

PMT = $500 (the quarterly payments)
r = 12% (the annual interest rate)
n = 4 (the number of compounding periods per year)
t = 10 (the number of years)

Plugging in these values, we get:

FV = $500 x [((1 + 0.12/4)^(4*10) - 1) / (0.12/4)]
FV = $19,222.34

Therefore, the account has a value of $19,222.34 at the end of 10 years. However, we need to add to this the value of the additional $500 that Bram invests at the end of the last quarter. To find the future value of this single investment, we can use the formula for future value of a lump sum:

FV = PV x (1 + r/n)^(n*t)

where:

PV = $500 (the present value of the investment)
r = 12% (the annual interest rate)
n = 4 (the number of compounding periods per year)
t = 10 + 1/4 (since the investment is made at the end of the last quarter)

Plugging in these values, we get:

FV = $500 x (1 + 0.12/4)^(4*(10+1/4))
FV = $18,478.27

Therefore, the total value of the account is:

$19,222.34 + $18,478.27 = $37,700.61

So, the closest answer is B, $37,700.60.

Bram Johnson Invests $500 at the End of Each Quarter