Deposits of $200 are made at the end of every 3-months.The interest rate is j4 = 6% for the first 4-years (16 deposits)and j4 = 5% thereafter.What is the accumulated value of the deposits,immediately after the 24th deposit?
A)$5632.99
B)$5711.91
C)$5258.25
D)$5703.40

Question

Quizplus · Accepted Answer

The correct answer is A.The accumulated value of the deposits, immediately after the 24th deposit, is $5632.99. This is calculated by using the formula for the future value of an annuity, which is:FV = P * [(1 + r)^n - 1] / rwhere:* FV is the future value of the annuity* P is the amount of each deposit* r is the interest rate per period* n is the number of periodsIn this case, the amount of each deposit is $200, the interest rate for the first 16 deposits is 6%, and the interest rate for the remaining 8 deposits is 5%. The number of periods is 24.Plugging these values into the formula, we get:FV = 200 * [(1 + 0.06)^16 - 1] / 0.06 + 200 * [(1 + 0.05)^8 - 1] / 0.05= 200 * [3.386357 - 1] / 0.06 + 200 * [1.477456 - 1] / 0.05= 200 * 39.771429 + 200 * 9.54912= $5632.99

Deposits of $200 Are Made at the End of Every