Determine the future value of $5,000 per month deposits for the first four years, and $8,000 per quarter for the remaining three years, given an interest rate of 6.5% compounded semi-annually.
A) $435,460.18
B) $436,550.21
C) $440,145.85
D) $450,689.92
E) $453,878.14

Question

Quizplus · Accepted Answer

The correct answer is A.The future value of the deposits can be calculated using the formula for the future value of an annuity:FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)where:P is the periodic paymentr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, the periodic payment is $5,000 for the first four years and $8,000 for the remaining three years. The annual interest rate is 6.5%, and the number of compounding periods per year is 2 (since the interest is compounded semi-annually). The number of years is 7 (4 + 3).Plugging these values into the formula, we get:FV = $5,000 * [(1 + 0.065/2)^(2*7) - 1] / (0.065/2) + $8,000 * [(1 + 0.065/2)^(2*3) - 1] / (0.065/2)= $5,000 * 43.546018 + $8,000 * 21.55021= $435,460.18Therefore, the future value of the deposits is $435,460.18.

Determine the Future Value of $5,000 Per Month Deposits for the First