SOLUTION: Given $400,000 today, determine the equivalent series of 24 semi annual payments which could be generated beginning in 6 months. Assume interest can be earned at a rate of 7 percen

Question 1164349: Given $400,000 today, determine the equivalent series of 24 semi annual payments which could be generated beginning in 6 months. Assume interest can be earned at a rate of 7 percent per year compounded semi annually.
where A= Present value of annuity 400,000
i= interest rate per period = 0.07/2 = 0.035
n = number of annuity
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a financial calculator makes this pretty easy.
it is an annuity with payments at the end of each time period, with each time period being equal to half a year, with a half a year being equivalent to 6 months.

using the financial calculator, you would provide the folloiwng information.
present value = -400,000.
future value = 0
interest rate = 7% per year / 2 = 3.5% per semi-annual period.
payments are made at the end of each semi-annual period.
number of semi-annual time periods is 24.

you would provide these inputs and then have the calculator tell you what the semi-annual payments need to be.

those semi-annual payments need to be equal to 24,909.13.
since they are made at the end of each semi-annual period, then the first payment is at the end of the first semi-annual period which is 6 months from the time of the investment.

this is what the calculator displays after the inputs are made and the PMT button is pressed.

there is a formula that you can do this manually with using your calculator.
that formula is:

ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.

using that formula, you would do the following:
p = 400000
r = .035
n = 24

the formula becomes a = (400000*.035)/(1-(1/(1+.035)^24))
execute the formula on your calculator to get:
p = 24909.1321
round to 2 decimal digits and the answer is the same as given by the calculator.

i used exel to verify this is correct.

the excel printout is shown below:

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