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?
We can use the formula for monthly compound interest:
FV = PMT * (((1 + r/n)^(n*t)) - 1) / (r/n)
where:
FV = future value (106,920)
PMT = monthly deposit (what we want to find)
r = annual interest rate (5.2%)
n = number of times compounded per year (12 for monthly)
t = time in years (19)
Plugging in the values and solving for PMT, we get:
106,920 = PMT * (((1 + 0.052/12)^(12*19)) - 1) / (0.052/12)
PMT = 185.29
Therefore, you should deposit $185.29 each month to reach a college fund of $106,920 after 19 years with an interest rate of 5.2% compounded monthly.
Nope, the bot is wrong again
i = .052/12 = .0043333...
n = 12*19 = 228
106,920 = paym( 1.0043333...^228 - 1)/.004333...
paym = $275.76 per month
My apologies for the mistake in my previous response. You are correct. Using the correct formula and values, the monthly deposit needed to reach a college fund of $106,920 after 19 years with an interest rate of 5.2% compounded monthly is $275.76 per month. Thank you for correcting me.
To determine how much you should deposit each month to achieve a future value of $106,920 in 19 years with an interest rate of 5.2% compounded monthly, you can use the formula for the future value of an ordinary annuity:
Future Value = Payment × [(1 + interest rate)^(number of periods) - 1] / interest rate
In this case, the future value is $106,920, the interest rate is 5.2%, and the number of periods is 19 years * 12 months/year = 228 months. We need to solve for the payment.
Rewriting the formula, we have:
Payment = Future Value × (interest rate / [(1 + interest rate)^(number of periods) - 1])
Now, substitute the values into the formula:
Payment = $106,920 × (0.052 / [(1 + 0.052)^(228) - 1])
Using a calculator or spreadsheet software, calculate the value of the formula:
Payment ≈ $398.49
Therefore, to achieve a future value of $106,920 in 19 years with an interest rate of 5.2% compounded monthly, you should deposit approximately $398.49 each month.