at the end of the 8 year period, the forest has no further value.
the company wants to earn 6% on its initial investment and also wants to set up a sinking fund to replace the purchase price.
if money is placed in the fund at the end of each year and earns 4% compounded annually, find the yearly payment.
the present value of the investment is the present value of 60,000 annual payments at the end of each year at 6% compounded annually.
the present value is therefore equal to $372,587.63 rounded to 2 decimal places.
that's the amount that you have to invest initially.
this amount will return 60,000 per year for 8 years if it earns 6% a year on that investment.
if you want to replace the purchase price at the end of the 8 year period and are making payments at 4% per year compounded annually, then you would have to put $40,436.13 into the fund at the end of each year.
you can use a financial calculator to do this, or you can use manual formulas.
if you are using a calculator, you would do something like the following:
to determine the initial investment:
present value (pv) = 0
future value (fv) = 0
number of time periods (ntp or np) = 8
interest rate percent per time period (r%) = 6
payments per time period (pmt) = 60000
payments are set to be made at the end of each time period.
you would then have the calculator find the present value for you by clicking on the PV button.
the present value will be negative because that's what you shell out initially.
the payments will be positive because that's what you get back at the end of each time period.
i used an online calculator to show you.
these are your inputs:
this is the output.
to determine how much you have to invest at the end of each year in order to replace the original purchase price:
present value (pv) = 0
future value (fv) = 372587.63
number of time periods (ntp or np) = 8
interest rate percent per time period (r% or ir%) = 4
payments are set to be made at the end of each time period.
you would then have the calculator find the payment for you by clicking on the PMT button.
the future value will be positive because that's what you get back.
the payments will be negative because that's what you shell out at the end of each time period.
these are your inputs:
this is your output.
if you choose to use manual formulas, then the following reference will guide you.
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes
the particular formula you would use to find the initial investment is:
PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
p = (a*(1-1/(1+r)^n))/r
p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods.
the particular formula you would use to find the annual payments 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 you use these formulas:
the interest rate per time period is not the percent.
it is the decimal eqivalent of the percent.
6% would become .06
4% would become .04
also, you enter all values as positive.
none of this negative positive business that is used with the financial calculators.
you can use your scientific calculator to solve these formulas.
just make sure you use the parentheses exactly as shown.
i confirmed both formulas will give you the same results that the financial calculators gave you.
as an exercise, you can do the same confirmation yourself.
let me know if you have any difficulty getting the same results manually,or understanding what transpired.