Today is Janet’s 23rd birthday. Starting today, Janet plans to begin saving for
ID: 2813394 • Letter: T
Question
Today is Janet’s 23rd birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $2,000 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 8 percent. How much will Janet expect to have in her account on her 65th birthday? Round your answer to 2 decimal places; for example 2345.25.
Explanation / Answer
Payment = 2,000
Rate of return = 8%
As payment is occuring at beginning of year and payment value = 2,000
Number of Payments = 42
Future value of payment = 2,000 * (1 + 8%)42 + 2,000 * (1 + 8%)41 + 2,000 * (1 + 8%)40 +.......+ 2,000 * (1 + 8%)
Future value of payment = 50,678.96 + 46,924.97 + ....+ 2,160
Future value of payment = 657,166.01
We can also calculate by annuity due formula
FV = (1 + r) * Payment * ((1 + r)time - 1)/ r
FV = (1 + 8%) * 2,000 * ((1 + 8%)42 - 1)/ 8%
FV = 1.08 * 2,000 * 24.339482/ 8%
FV = 657,166.01
we will calculate future value of 10,000 also.
FV = 10,000 * (1.08)42
FV = 253,394.82
Total value on 65th birthday = 657,166.01 + 253,394.82
Total value on 65th birthday = 910,560.83
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