Mr. Arya wants to know the amount he should pay for a gold mine expected to yield an annual return of ₹ 4 lakh for the next 10 years, after which it will be worthless. Find the amount he should pay for the mine, if he wants to yield 18% annual return on his investment and also set up a sinking fund to replace the purchase price. Assume that the sinking fund earns 10% annually. [Use $(1 \cdot 1)^{10} = 2 \cdot 5937$ ]

Answer: Mr. Arya should pay approximately ₹ 16,47,800.7 for the gold mine.

Step-by-step solution

Step 1: Define variables and formula for sinking fund

First, we define all the given variables: the annual return, the desired investment return rate, the sinking fund interest rate, and the number of years. We also state the formula for the annual sinking fund contribution, $S$ , which is needed to accumulate the purchase price $P$ over $n$ years at an interest rate $r$ .

Step 2: Calculate annual sinking fund contribution

Now, we substitute the given values into the sinking fund formula. We use the provided value for $(1.1)^{10}$ to calculate the annual contribution $S$ as a fraction of the purchase price $P$ .

Step 3: Formulate the annual net return equation

The annual net return available to Mr. Arya is the total annual return from the mine minus the amount set aside for the sinking fund. This net return must equal the desired 18% annual return on his initial investment $P$ .

Step 4: Solve for the purchase price P

We substitute the expression for $S$ into the net return equation. Then, we rearrange the equation to solve for $P$ , the purchase price. This involves combining terms with $P$ and dividing by the coefficient of $P$ .

Solve your own maths question free →