Question 1179839
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 <a href = "https://arachnoid.com/finance/index.html" target = "_blank">https://arachnoid.com/finance/index.html</a>


here's the inputs.


<img src = "http://theo.x10hosting.com/2021/050501.jpg" >


here's the output.


<img src = "http://theo.x10hosting.com/2021/050502.jpg" >


as you can see, the payment required is the same at 2801.07 when rounded to the nearest penny.