SOLUTION: Aaron wants to start a retirement fund that will have $500,000 in it when he retires in 25 years. He wants to achieve this goal by making semiannual (twice per year) payments in
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-> SOLUTION: Aaron wants to start a retirement fund that will have $500,000 in it when he retires in 25 years. He wants to achieve this goal by making semiannual (twice per year) payments in
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Question 1179839: Aaron wants to start a retirement fund that will have $500,000 in it when he retires in 25 years. He wants to achieve this goal by making semiannual (twice per year) payments into a fund that earns 9% interest compounded semiannually. How much should his payments be?
Round your final answer to the nearest cent.
Can you please explain to me this third homework question step-by step? Thank you once again!
You can put this solution on YOUR website! he wants 500,000 in the account in 25 years.
he will be making payments at the end if each 6 month period.
the interest rate is 9% per year compounded semi-annually.
the interest rate per semi-annual period = 9% / 2 = 4.5%.
the number of semi-annual periods will be 25 * 2 = 50.
this can be solved by calculator or by formula.
the formula is:
ANNUITY FOR A FUTURE AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (f * r)/((1 + r) ^ n-1)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.
when f = 500,000 and r = .045 and n = 50, the formula becomes:
a = (500000 * .045)/((1 + .045) ^ 50 - 1)
solve for a to get:
a = 2801.072928
that's the semi-annual payment required.
with a calculator, you should get the same answer.
