Jane and John are twins. After graduating from college on their 21st birthday, J

Question

Jane and John are twins. After graduating from college on their 21st birthday, Jane takes a job and immediately starts investing $300 a month (end of month) to a stock mutual fund. She does this for 8 years (96 months) until her 29th birthday when she gets married and finds more pressing uses for her money. John marries his college sweetheart and starts a family and does not start investing until his 29th birthday (8 years after graduating, just as his sister stops investing). At this point he contributes $300 a month (end of month) to the same stock mutual fund as his sister and continues to do so each month until he retires on his 65th birthday (432 months).

a.      Determine how much Jane and John will each have contributed to their retirement in terms of a simple sum of their contributions (i.e., no time value of money and no interest)

b.     Assuming the stock mutual fund produces 9.0% a year (APR) return (compounded monthly). Which of the twins has the larger balance in his/her mutual fund account when they turn 65? Determine the balances for each of them.

Explanation / Answer

Contribution by Jane as simple suim of contribution = 300* 12* 8 = 28,800
Contribution by John as simple suim of contribution = 300* 36*12 = 129,600

Rate per Month =9%/12
FV of Jane's Contribution at age 29 = 300*((1+r)n-1)/r = 300*((1+9%/12)96-1)/9%/12 = 41956.85
FV of Jane's Contribution at age 65 = 41956.85 * (1+9%/12)432 = 1058440.73

FV of John's Contribution at age 65 = 300*((1+r)n-1)/r = 300*((1+9%/12)432-1)/9%/12 = 969075.52

Jane's Contribution is higher

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