Billy deposits $500 every 3-months in a fund earning interest at j₄ = 8%.After 24 deposits,the interest rate changes to j₄ = 6%.What is the accumulated value at the time of the 40^th deposit?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the future value of an annuity:

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

where FV is the future value, PMT is the periodic deposit, r is the interest rate per period, and n is the number of periods.

For the first 24 deposits, we have:

PMT = 500
r = 8%/4 = 2% (since there are 4 quarters in a year)
n = 24

Plugging these values into the formula, we get:

FV = 500 * ((1 + 0.02)^24 - 1) / 0.02 = $14,213.08

Note that we subtract 1 from the expression (1 + 0.02)^24 to account for the fact that the first deposit doesn't earn any interest.

For the remaining deposits, we have:

PMT = 500
r = 6%/4 = 1.5%
n = 16

Using the same formula, we get:

FV = 500 * ((1 + 0.015)^16 - 1) / 0.015 = $14,055.55

To find the total accumulated value at the time of the 40th deposit, we simply add these two values:

FV = $14,213.08 + $14,055.55 = $28,268.64

Therefore, the answer is $28,268.64, which corresponds to choice (C).

Billy Deposits $500 Every 3-Months in a Fund Earning Interest