Question

In: Finance

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

Today is Janet’s 23rd birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $1,000 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 9 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.

Solutions

Expert Solution

Current balance in account = 0

One time gift from Aunt on 23rd Bday = $10,000.

Annual investment from 23nd bday     = $1000.

Annual rate of return in account           = 9% p.a.

** the one time gift in the account will grow at 9% for 42 years and the annual investment in the account will grow for respective number of years. the annual investment of $1000 on 23nd bday will grow for 42 years, annual investment on 24th bday will grow for 41 years and so on.

Value of investment on 65th bday = P*(1+r)^t + [{P(1+r)^n -1} /I](1=i)

                                                       = 10000 (1.09)^42 + {1000(1.09)^42-1/0.09 }(1.09)

                                                       = 373175.3 + 439845.7

                                                       = $8,13,021 /-


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