You intend to create a college fund for your baby. If you can get an interest rate of 6.8% compounded monthly and want the fund to have a value of 145,157 after 19 years, how much should you deposit each month? Round to the nearest cent.
We can use the formula for the future value of an annuity:
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)
where FV is the future value, PMT is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Plugging in the given values, we get:
145157 = PMT * [(1 + 0.068/12)^(12*19) - 1] / (0.068/12)
Solving for PMT, we get:
PMT = 145157 * (0.068/12) / [(1 + 0.068/12)^(12*19) - 1]
PMT ≈ $292.14
Therefore, you should deposit approximately $292.14 each month to reach a college fund value of $145,157 after 19 years, assuming an interest rate of 6.8% compounded monthly.
To determine how much you should deposit each month, you can use the formula for the future value of an annuity:
Future Value = Deposit Amount × ((1 + Monthly Interest Rate)^(Number of Compounding Periods) - 1) / Monthly Interest Rate
In this case, the future value is $145,157, the monthly interest rate is 6.8% / 12 = 0.5667%, and the number of compounding periods is 19 years × 12 months/year = 228 months.
Plugging in these values into the formula, we get:
$145,157 = Deposit Amount × ((1 + 0.5667%)^(228) - 1) / 0.5667%
To solve for the deposit amount, we can rearrange the formula:
Deposit Amount = $145,157 × 0.5667% / ((1 + 0.5667%)^(228) - 1)
Calculating the deposit amount, we get:
Deposit Amount ≈ $145,157 × 0.5667% / ((1 + 0.5667%)^(228) - 1)
Deposit Amount ≈ $145,157 × 0.005667 / ((1 + 0.005667)^(228) - 1)
Deposit Amount ≈ $824.32
Therefore, you should deposit approximately $824.32 each month for 19 years in order to have a college fund value of $145,157.