A company sets up a sinking fund to accumulate ₹1,00,000 in 4 years to replace a machine, by depositing an equ

Worked Examples · Example 11

Q. A company sets up a sinking fund to accumulate ₹1,00,000 in 4 years to replace a machine, by depositing an equal amount at the end of each year into a fund earning 10% per annum compounded annually. Find the annual deposit. [Given (1.1)^4 = 1.4641]

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The fund must accumulate $A=₹1{,}00{,}000$ in $n=4$ years at $i=0.10$ . Solve the accumulated-value formula for the deposit $C$ :

C=A\left[\frac{i}{(1+i)^{n}-1}\right]=100000\left[\frac{0.1}{(1.1)^{4}-1}\right]=100000\left[\frac{0.1}{1.4641-1}\right]=100000\times\frac{0.1}{0.4641}=\frac{10000}{0.4641}\approx ₹21{,}547.08.

Check (independent verification): put this deposit back into the accumulated-value formula: …

Q.A company sets up a sinking fund to accumulate ₹1,00,000 in 4 years to replace a machine, by depositing an equal amount at the end of each year into a fund earning 10% per annum compounded annually. Find the annual deposit. [Given (1.1)^4 = 1.4641]