Grandma Chloe wants to help Trymaine while he's in college by giving him a $\$ 250$ monthly allowance for 4 years of college out of an account that earns $3.4 \%$ interest compounded monthly.

How much must Chloe have in the account for Trymaine to receive the $\$ 250$ payments for 4 years?

If Chloe began making monthly deposits into the account 13 years ago, how much were her monthly deposits?
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Step 1 ：Use the formula for the future value of an ordinary annuity: \(FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)\)

Step 2 ：Substitute the given values into the formula: \(FV = 250 \times \left( \frac{(1 + 0.0028333)^{48} - 1}{0.0028333} \right)\)

Step 3 ：Calculate the expression to find the future value (FV): \(FV \approx 12,607.84\)

Step 4 ：Therefore, Chloe must have at least $12,607.84 in the account for Trymaine to receive the $250 payments for 4 years.

Step 5 ：Use the formula for the present value of an ordinary annuity: \(PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)\)

Step 6 ：Substitute the given values into the formula: \(12,607.84 = P \times \left( \frac{1 - (1 + 0.0028333)^{-156}}{0.0028333} \right)\)

Step 7 ：Solve the equation for P to find the monthly deposits Chloe has been making: \(P \approx 50.00\)

Step 8 ：Therefore, Chloe has been making monthly deposits of $50.00 into the account for the past 13 years.