Question

Suppose that a family wants to start a college fund for their child. If they can get a rate of 5.2%, compounded monthly, and want the fund to have a value of $55,500 after 20 years, how much should they deposit monthly? Assume an ordinary annuity and round to the nearest cent.

Answer 1

To calculate the monthly deposit needed for the college fund, we can use the formula for the future value of an ordinary annuity. Plug in the values and solve for P to find the monthly deposit.

Step-by-step explanation:

To calculate the monthly deposit needed for the college fund, we can use the formula for the future value of an ordinary annuity:

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

Where:

FV is the desired future value of the fund, which is $55,500

P is the monthly deposit we want to find

r is the monthly interest rate, which is the annual interest rate of 5.2% divided by 12

n is the number of compounding periods, which is 20 years multiplied by 12 months

Plugging in the values, we have:

$55,500 = P * ((1 + 0.052/12)^(20*12) - 1) / (0.052/12)

Simplifying the equation, we can solve for P:

$55,500 * (0.052/12) = P * ((1 + 0.052/12)^(20*12) - 1)

P = $55,500 * (0.052/12) / ((1 + 0.052/12)^(20*12) - 1)

Using a calculator or spreadsheet software, we can evaluate this expression to find the monthly deposit needed.

Answer 2

The answer for Edg. is A.) 131.93