Erika and Kitty, who are twins, just received $10,000 each for their 22th birthd

Question

Erika and Kitty, who are twins, just received $10,000 each for their 22th 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 fund that invests in high quality bonds whose investors have earned 8% per year in the past. Kitty invested in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors on average have earned 13% per year in the fund's relatively short history. Round all answers to the nearest hundredth


a. If Erika's funds earn the same returns in the future as in the past, how old will she be when she becomes a millionaire?
years

b. If Kitty's funds earn the same returns in the future as in the past, how old will she be when she becomes a millionaire?
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?

Explanation / Answer

a.) 35.18729 years

b.) 26.65815 years

c.) $11,798.29

The formula to find the value of your ordinary annuity is:
= Payment [((1+r)^n)-1]/r
where r = your interest rate

So you want to find out n when the value is 1 million

1,000,000 = 5,000 ((1+8%)^n)/8%
1,000,000 = 62,500[(1.08^n)-1]
16 = 1.08^n - 1

15 = 1.08^n

log15/log1.08 = n
n = 35.18729

for part B.. you do the same thing but with an interest rate of 13%

1,000,000 = 5,000 [((1+13%)^n)-1]/13%

1,000,000 = 38,461.54[(1.13^n)-1]

26 = 1.13^n -1

25 = 1.13^n

log25/log1.13 = n

n = 26.65815

for Part C... now you have n which is the same as from part B, but now you need to find the size of the payment so,

1,000,000 = x[((1+.08)^26.65815)-1)/8%]

1,000,000 = x[7.780646 -1]/.08 = 84.75807x

x = $11798.29

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