SOLUTION: For a nominal annual interest rate of 2.3% compounded monthly, find the present value of an annuity of $175 at the end of each month for eight months and $280 thereafter at the end
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Question 1152009: For a nominal annual interest rate of 2.3% compounded monthly, find the present value of an annuity of $175 at the end of each month for eight months and $280 thereafter at the end of each month for further two years. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the annuity is 175 at the end of each month for a total of 8 months + 24 months = 32 months.
the annual interest rate is 2.3% per year.
the monthly interest rate is (2.3 / 12)% per month.
you would use a financial calculator to find the present value for 8 months and then for 24 months, and then you would find the present value of the present value for 24 months as shown below.
first get the present value of 175 at the end of each month for 8 months.
the annuity will be present worthed to time point 0.
that will be equal to a present value of 1,388.00
next get the present value of 180 at the end of each month for 24 months.
the annuity will be present worthed to time point 8.
that will be equal to a present value of 4,218.20
now take the present value of the future value of 4,218.20 for 8 months.
that makes all values present worthed to time point 0.
that will be equal to 4,154.08
now take the sum of 1388.00 and 4154.08.
that will be equal to 5542.08.
that's your present value for both those annuities at time point 0.
the first annuity was present worthed to time point 0.
the second annuity was present worthed to time point 8.
then the present worth from time point 8 was present worthed to time point 0.
that made the present value of both annuities equal to the common time point of 0.
i also did a cash flow analysis using excel.
the result of that cash flow analysis supported the method used with the financial calculator.
note:
when using the financial calculator, the percent is used.
when using excel, the rate is used.
the rate is the percent divided by 100.
here's the results of using the financial calculator.
here's the results using excel for the cash flow analysis.
