We can solve this problem using the financial calculator method, applying the formula for a deferred annuity.

Given data:

• Present Value (PV) = $40,000 (the initial investment)
• Interest rate (i) = 3.00% compounded monthly (which is 3% / 12 months = 0.25% per month)
• Number of periods for annuity payments (n) = 4 years × 12 months = 48 months
• Deferred period = 14 years (deferred for 14 years means payments begin after 14 years)

Step-by-step solution:

1. Find the future value (FV) after the 14 years of deferral. The account will earn interest for 14 years before the monthly payments begin. So, we will first calculate the future value of the $40,000 after 14 years, using the compound interest formula:

$FV = PV \times (1 + i)^n$

Where:

• $PV = 40,000$
• $i = 0.25\%$ (0.0025 per month)
• $n = 14 \times 12 = 168$ months (14 years)

$FV = 40,000 \times (1 + 0.0025)^{168}$

2. Then calculate the monthly payment (PMT) during the 48 months of college. After 14 years, the future value of the investment is used to determine the size of the monthly payments for the next 48 months. The formula for the monthly payment in an ordinary annuity (with payments made at the beginning of each period, which is an annuity-due) is:

$PMT = \frac{FV \times i}{(1 - (1 + i)^{-n})}$

Where:

• $FV$ = future value after 14 years
• $i = 0.0025$ (monthly interest rate)
• $n = 48$ months (college duration)

Let's calculate the values step by step.

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Let me calculate this for you! Given data PV = 40000 # initial investment annual_interest_rate = 0.03 # 3% annual interest monthly_interest_rate = annual_interest_rate / 12 # monthly interest rate (compounded monthly) years_deferred = 14 # deferred period in years payment_duration_years = 4 # payment period in years months_deferred = years_deferred * 12 # deferred period in months months_payment = payment_duration_years * 12 # payment period in months

Calculate the future value (FV) after the 14-year deferral period

FV = PV * (1 + monthly_interest_rate)**months_deferred

Calculate the monthly payment (PMT) using the annuity formula for an annuity-due (beginning of period)

PMT = FV * monthly_interest_rate / (1 - (1 + monthly_interest_rate)**(-months_payment))

Round the monthly payment to the nearest cent

PMT_rounded = round(PMT, 2)

PMT_rounded # Resulting monthly paymentThe size of the monthly payments, after the 14-year deferral period, will be $1,346.80.

Let me know if you need further details or clarifications!

Here are some related questions you might find useful:

1. How would the monthly payment change if the interest rate was higher (e.g., 5%)?
2. What would happen to the monthly payment if the annuity period were longer (e.g., 6 years)?
3. How can we calculate the present value of an annuity given a set monthly payment?
4. What is the difference between an ordinary annuity and an annuity-due in terms of payment timing?
5. How can you calculate the future value of an investment using a financial calculator?

Tip: When dealing with annuities, always make sure to note whether the payments are at the beginning (annuity-due) or at the end (ordinary annuity) of each period, as it significantly impacts the calculation.