Posted by **Gibbons** on Monday, June 21, 2010 at 8:17am.

A company is considering the purchase of a forest that is estimated to yield an annual return of $50,000 for 10 years, after which the forest will have no value. The company wants to earn 8% on its investment and set up a sinking fund to replace the purchase price. If the money is placed in the fund at the end of each year and earns 6% compounded annually, find the price the company should pay for the forest.

- Math? Definitely not "college" -
**Writeacher**, Monday, June 21, 2010 at 8:22am
Please type your __subject__ in the **School Subject** box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.

- future values -
**MathMate**, Monday, June 21, 2010 at 3:13pm
If I understand the investment instructions correctly, this is how it works:

The company would invest an amount P which should yield net 8% return each year for 10 years.

The revenue generated is constant each year at $50,000, and includes profit and capital repayment. The capital is repaid from a sinking fund that pays 6% p.a. and should generate the original capital at the end of 10 years. The annual payment into the sinking fund (out of the revenue) is $x.

In short,

P=initial investment

x=annual investment into sinking fund

For the 8% profit over 10 years, we have

P*(0.08*10) = 50000*10 - 10x ...(1)

and that the amount x over 10 years at 6% p.a. should yield exactly P:

P = x*1.06^10/(1.06-1.0) ...(2)

Substituting (2) into (1)

x*1.06^10/(1.06-1.0)*(0.08*10) = 50000*10 - 10x

Solve for x to get $14758.85

and from (2)

P = $440514.32

Substitute the amounts into the scenarios and check.

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