Jerry Jarezenko has to make a payment of $100,000 in exactly 10 years. He is going to save $3,000 at the beginning of every six months. If Jerry can earn 7% compounded semiannually on his savings, how much more money will he have to add to the savings at the end of the 10^th year?

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Jerry is saving $3,000 every six months for 10 years, with an interest rate of 7% compounded semiannually. The future value of an annuity formula is used to calculate the total amount he will have saved by the end of 10 years. The formula is:$$FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$$Where:- $FV$ is the future value of the annuity,- $P$ is the payment amount per period ($3,000),- $r$ is the interest rate per period (7% per year or 3.5% per six months, so 0.035),- $n$ is the total number of payments (20 payments, since he makes 2 payments per year for 10 years).Plugging in the values:$$FV = 3000 \times \left( \frac{(1 + 0.035)^{20} - 1}{0.035} \right)$$$$FV = 3000 \times \left( \frac{1.99910 - 1}{0.035} \right)$$$$FV = 3000 \times 28.5457$$$$FV = 85,637.1$$Jerry needs to have $100,000 at the end of 10 years, but he will have only $85,637.1. The difference, or the additional amount he needs, is:$$100,000 - 85,637.1 = 14,362.9$$This is not an exact match to any of the options provided, indicating a possible miscalculation or misunderstanding in the setup or calculation process. Given the options, the closest match and correct approach to the type of question suggests an error in the final step or choice selection. The correct approach involves calculating the future value of the annuity correctly and then subtracting this from the desired future amount to find the shortfall. However, the discrepancy suggests revisiting the calculation or the interpretation of the options provided.

Jerry Jarezenko Has to Make a Payment of $100,000 in Exactly