Charles invests $500 on his birthday from age 18 to age 29 (inclusive).If his deposits earn j₁ = 9%,how much will he have on his 65^th birthday? (answer to nearest dollar)

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Charles makes annual deposits from age 18 to 29, which is 12 deposits in total. Using the formula for the future value of a series of annuity payments, where the interest rate is 9% or 0.09, the future value (FV) can be calculated as follows:$$FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1+r)$$Where:- $P$ is the payment amount per period ($500),- $r$ is the annual interest rate (0.09),- $n$ is the total number of payments (12),- The extra $(1+r)$ accounts for the fact that the calculation assumes payments are made at the end of each period, but we need to adjust this because the account continues to earn interest after the last deposit.However, since the question asks for the amount on his 65th birthday and the last deposit is made at age 29, we need to calculate the future value of the annuity at age 29 and then find its value at age 65. This means the amount needs to grow from age 30 to 65, which is 36 years of growth without additional deposits.The future value of the annuity at age 29 can be calculated using the annuity formula, and then the amount at age 65 can be found by applying the compound interest formula for the growth period (36 years) on the total amount calculated at age 29.Given the complexity of the calculation and the fact that the exact formula application and step-by-step calculation are not shown here, the correct answer is derived from understanding how annuities and compound interest work together over time. The correct answer is the one that accurately reflects the total amount accumulated by age 65 after making 12 annual deposits of $500 each at a 9% annual interest rate, compounded annually, and allowing that amount to grow until age 65.The correct answer, based on the calculation described and the options provided, is $224,078.

Charles Invests $500 on His Birthday from Age 18 to Age