When Cody's son was born, he put $4,500 in an investment that earns 7% compounded semi-annually. This investment will mature when his son turns 18 and will go straight into an annuity at 4.75% compounded and paying out quarterly at the end of the period. The investment was to help pay for his 4-years of college. Find the size of these quarterly payments received by Cody's son during his college stay.

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http://www.1728.com/annuity2.htm

at age 18:

the amount of the investment = the present value of the annuity
4500(1.035)^36 = x(1 - 1.011875^-16)/.011875
15526.20 = x(14.4938741)
x = 15526.20/14.4938741 = 1071.22

did u look it up???

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the answer is 45 done this in year 5 mate. simples

To find the size of the quarterly payments received by Cody's son during his college stay, we need to calculate the future value of the investment after it matures when his son turns 18. Then, we can calculate the size of the quarterly payments using the future value of the investment and the annuity formula.

First, let's calculate the future value of the investment after it matures when Cody's son turns 18. We can use the compound interest formula:

Final Amount = Principal * (1 + (Interest Rate/Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)

In this case, the principal is $4,500, the interest rate is 7% (0.07), and the investment compounds semi-annually for 18 years. So, the calculation will be:

Final Amount = $4,500 * (1 + (0.07/2))^(2 * 18)

Next, we can calculate the size of the quarterly payments received using the future value of the investment and the annuity formula:

Quarterly Payment = Future Value * (Interest Rate/Number of Compounding Periods) / (1 - (1 + (Interest Rate/Number of Compounding Periods))^(-Number of Compounding Periods * Number of Years))

In this case, the future value is the result from the previous calculation, the interest rate is 4.75% (0.0475), and the annuity pays out quarterly. Assuming Cody's son will be in college for 4 years, the calculation will be:

Quarterly Payment = Final Amount * (0.0475/4) / (1 - (1 + (0.0475/4))^(-4 * 4))

Solving this equation will give us the size of the quarterly payments received by Cody's son during his college stay.