Question 1119945: Shahab has an opportunity to invest in a fund which earns 6% profit compounded annually. How much should he invest now if he wants to receive Rs.6, 000(including principal) from the fund, at the end of each year for the next 10 years? How much interest he would earn over the period of 10 year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can use this online calculator to get your results.
https://arachnoid.com/finance/
here's the results.
he would have to invest 44,160.52 today in order to get 6,000 at the end of each year for the next 10 years.
your inputs are:
future value = 0.
payment = 6,000.
payment at the end of each year.
interest rate = 6% per year.
number of periods = 10.
you click on PV and the calculator tells you what the present value needs to be.
you could also use excel.
here's the results of using that.
in the use of excel, two formulas could be used.
they are PV formula and NPV formula.
PV formula assumes the same annual amount each year.
NPV formula assumes they could be different, although, in this case, they are not.
when the annual amounts are the same, NPV and PV will give the same results, assuming the same assumptions go into each.
the interest he earns over the 10 year period is based on assumption about what he does with the money he receives at the end of each year.
if he takes that 6,000 that he gets at the end of each year and invests is at the same interest rate of 6% per year, he would have 79,084.77 at the end of the 10 year period.
his total interest earned would be 79084.77 minus 44160.52 = 34,924.25.
this is equivalent to the future value of those same payments as shown in the following calculations.
in this calculatin, the present value is 0 and the future value is 0 and the payments are 6000 at the end of each year and you click on FV of those payments.
this is also equivalent to the future value of the present value calculated earlier, as shown in the following calculations.
in this calculation, the prewent value is 44160.52 and the future value is 0 and the payments at the end of each year are 0 and you click on FV which then give you the future value of the present value.
payments at the end of each year are not involved in this calculation.
in all likelihood, he does not reinvest the 6000, since why would he draw the money out at the end of each year only to re-invest it. in that case, he would just have put the money in the bank and let it accumulate for the 10 year period, which is the last calculation shown above.l
in all likelihood, he would take the money out at the end of each year and use it for something else.
in that case, he received 6000 * 10 = 60,000 over the 10 year period on an initial investment of 44160.52.
his interest earned is 60,000 minus 44,160.52 = 15,839.48.
this is based on the interest earned on the remaining balance at the end of each year as shown in the following excel year by year printout.
the total interest earned is the sum of the interest earned from the balance in the previous year in each of the 10 years of the loan period.
remaining balance at the end of the 10 year period is zero, as it should be.
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