Question

You intend to create a college fund for your baby. If you can get an interest rate of 5.2% compounded monthly and want the fund to have a future value of $106,920 after 19 years, how much should you deposit each month? A. $471.28 B. $5,411.06 C. $466.64 D. $275.76

Answer 1

$217.62

Explanation;

Given the following:

Amount A = $106,920

Time T = 19years

Rate R = 5.2% = 0.052

Time of compounding n = 1/12 years (monthly)

Required

Amout deposited (Principal)

Using the compound interest formula;

A = P(1+r/n)^nt

Substitute the given values

106, 920 = P(1+0.052(12))^(19/12)

106,920 = P(1+0.624)^1.5833

106,920 = P(1.624)^1.5833

106,920 = 2.1549P

P = 106,920/2.1549

P = 49,619.45

To get the amount to be deposited each month, we will divide the principal by 12 as shown.

Amount deposited each month = Principal/(12*19)

Amount deposited each month = 49,619.45/228

Amount deposited each month = $217.62