Today is Janet’s 23 rd birthday. Starting today, Janet plans to begin saving for

Question

Today is Janet’s 23rd
birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $3,000 to a brokerage account each year on her birthday. Her first contribution will take place today. Her 42nd and final contribution will take place on her 64th birthday. Her aunt has decided to help Janet with her savings, which is why she gave Janet $10,000 today as a birthday present to help get her account started. Assume that the account has an expected annual return of 10 percent. How much will Janet expect to have in her account on her 65thbirthday? Round your answer to 2 decimal places; for example 2345.25.

Explanation / Answer

Janet's Annual Contributions = $ 3000, Number of Annual Contributions = 42, Rate of Return = 10 % per annum, Janets Aunt's Contribution = $ 10000

Future Value of Janet's Contribution at age 65 = 3000 x (1.1)^(42) + 3000 x (1.1)^(41) + 3000 x (1.1)^(40) + ......+ 3000 x (1.1) = $ 1774202.075

Future Value of Janets Aunt's Contribution at age 65 = 10000 x (1.1)^(42) = $ 547636.992

Total Future Value of Contributions on Janet's 65th Birthday = 1774202.075 + 547636.992 = $ 2321839.07

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