Erika and Kitty, who are twins, just received $25,000 each for their 27th birthd
ID: 2804370 • Letter: E
Question
Erika and Kitty, who are twins, just received $25,000 each for their 27th birthdays. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her "early retirement fund on her birthday beginning a year from today. Erika opened an account with the Safety First Bond Fund a mutual und that n ests in high-quality bonds nose nvestors have earned % per earn e ast. Kitty invested in the New Issue Bio-Tech Fund, which invests in small newly issued bio tech stocks and whose investors have earned an average of 14% per year in the fund's relatively short history a. If Erika's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places. years b. If Kitty's fund earns the same returns in the future as in the past, how old will she be when she becomes a ilinaire? Round your answer to two decimal places years c. How large would Erika's annual contributions have to be for her to become a millionaire at the same age as Kitty, assuming their expected returns are realized? Round your answer to the nearest cent.Explanation / Answer
a.) To calculate when Erika will turn to be a millionaire, we will use future value of annuity concept,
5,000 x {(1+0.07)t -1)/0.07} =1,000,000
{(1.07)t -1)/0.07} = 200
(1.07)t -1 = 14
(1.07)t = 15
Taking log both sides,
t = log(15)/log(1.07)
t = 40.025 years
b.) To calculate when Kitty will turn to be a millionaire, we will use future value of annuity concept,
5,000 x {(1+0.14)t -1)/0.14} =1,000,000
{(1.14)t -1)/0.14} = 200
(1.14)t -1 = 14
(1.14)t = 15
Taking log both sides,
t = log(15)/log(1.14)
t = 20.668 years
c.) To become the millionaire at the same time as Kitty,
1,000,000 = P x {(1+0.14)20.6678 -1)/0.14}
1,000,000 = P x (15-1)/0.14
P = 1,000,000/100
P = 10,000
Hence, Erika's contribution has to be $10,000 per annum.
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