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 $ 2 0,000 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 65th birthday?

Answer 1

Janet's Periodic Contributions = $ 3000 and Account Interest Rate = 10%

Number of Deposits = 42

Therefore, Total Future Value(FV) of Janet's Contrbutions = F1 = 3000 x (1.1)^(42) + 3000 x (1.1)^(41) + 3000 x (1.1)^(40) + ......+ 3000 x (1.1)^(2) + 3000 x (1.1) = [{(1.1)^(42) - 1} / {1.1 - 1}] x 3000 ~ $ 1612910.98

Janets Aunt's Contribution = $ 20000 and Compounding Tenure = (65 - 23) = 42 years

Therefore, Aunts Contributions Future Value = F2 = 20000 x (1.1)^(42) = $ 1095273.98

Total Account Value on Janet's 65th Birthday = F1 + F2 = 1612910.98 + 1095273.98 = $ 2708184.96 ~ $ 2708185