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!
Answer by Theo(13342) (Show Source): 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.
i used the financial calculator at https://arachnoid.com/finance/index.html
here's the inputs.
here's the output.
as you can see, the payment required is the same at 2801.07 when rounded to the nearest penny.
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