Calculating Annual Payment for Debt Discharge
The problem requires finding the equal annual payment (annuity) that will pay off a debt over a specific period with compound interest. This is a present value of an ordinary annuity problem.
Annuity Formula
The formula for the present value (PV) of an ordinary annuity is:
$ PV = P \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] $Where:
- $PV$ = Present Value of the debt (₹1,025)
- $P$ = Annual Payment (what we need to find)
- $i$ = Interest rate per period (5% or 0.05)
- $n$ = Number of periods (2 years)
Applying the Formula
We need to rearrange the formula to solve for $P$:
$ P = \frac{PV}{\left[ \frac{1 - (1+i)^{-n}}{i} \right]} $Calculations
Substitute the given values into the formula:
- Calculate the term $(1+i)^{-n}$: $(1 + 0.05)^{-2} = (1.05)^{-2} \approx 0.907029479$
- Calculate the numerator $1 - (1+i)^{-n}$: $1 - 0.907029479 \approx 0.092970521$
- Calculate the expression in the square brackets (the annuity factor): $\frac{0.092970521}{0.05} \approx 1.85941042$
- Calculate the Annual Payment (P): $P = \frac{1025}{1.85941042}$ $P \approx 551.2523$
Final Answer
Rounding the result to two decimal places, the annual payment is ₹551.25.
Similar Questions
Four words have been given, out of which three are alike in some manner and one is different. Select the odd one.
Peacock, Woodpecker, Parrot, Bat
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Important Questions from Installments
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What annual instalment will discharge a debit of ₹5,664 in 4 years at 12% simple interest?
A sum of Rs. P was borrowed and paid back in two equal yearly instalments, each of Rs. 35,280. If the rate of interest was 5% compounded annually, then the value of P is:
