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Question 1194167: Person A plans for retirement by depositing $2 000 per year in a
superannuation fund each year for 10 years, starting when he turns 25 years
old, and then leaving the accumulated funds in his superannuation fund until
he turns 65. Person B wishes to have the same funds available on his
retirement at age 65 but does not begin to save until he turns 35 when he
also begins to make annual deposits into a superannuation fund, making the
first deposit on his 35th birthday and continuing until he retires making the last
deposit on his 65th birthday. Assuming their funds earn interest at an annual
rate of 7%, compounded annually, find the annual deposit needed to be made
by person B. Find how much more interest is earned by person A.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! person A invests 2000 on his 25th birthday until his 34th birthday.
on his 34th birthday he will have $27,632.90 in his account.
he will keep this in his account until his 65th birthday.
the interest rate he is earning on his investment is 7% per ear.
he will have $225,073.09 in his account on his 65th birthday.
person B starts investing each year starting on his 35th birthday and ending on his 65th birthday.
that makes 31 years of investing.
he needs to invest $2,205.02 each year for 31 years so that he can have $225,073.09 in his account on his 65th birthday.
the calculation required to determine the payment person B needs to make each year for 31 years was determined through the use of the ti-ba-ii business analyst calculator.
inputs were:
present value = 0
future value = 225,073.09
number of years = 31
interest rate per year = 7%
payments made at the end of each year.
output was:
payment made at the end of each year = 2205.019925.
this was rounded to 2205.02.
excel was used to do the year by year calculations required to demonstrate that the future value of the investment for person B was the same as the future value of the investment for person A.
that is shown below:
let me know if you have any questions.
theo
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