Jerry makes semi-annual deposits of $R into a fund paying j₂ = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R? A)$1470.10 B)$1506.85 C)$1675.13 D)$1717.01

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The correct answer is A because the future value of the semi-annual deposits on September 15, 2015 is $15,000. The future value of each deposit is $R * (1 + j2)^n, where j2 is the semi-annual interest rate and n is the number of semi-annual periods. The first deposit was made on March 15, 2011, and the last deposit will be made on March 15, 2015. There are 8 semi-annual periods between March 15, 2011, and September 15, 2015. The future value of the first deposit is $R * (1 + 0.05)^8 = $R * 1.47010. The future value of the last deposit is $R * (1 + 0.05)^0 = $R. The future value of all of the deposits is $R * 1.47010 + $R * 1.47010 + ... + $R * 1.47010 + $R = $R * 1.47010 * 8 = $15,000. Solving for R, we get R = $15,000 / 1.47010 = $1470.10.

Jerry Makes Semi-Annual Deposits of $R into a Fund Paying