Which one of the following is the amount of annuity of Rs. 1,400 for a year at 8% p.a. ? a) Rs. 1400 b) Rs. 1512 c) Rs. 1521 d) Rs. 2511

The annuity amount (future value of an annuity) is calculated using the formula:

$$A=P\times \frac{(1+r{)}^n-1}{r}$$

Where:

• $P=1,400$ (annual payment),
• $r=8\%=0.08$ (annual interest rate),
• $n=1$ (since the annuity is for one year).

Substitute the values: $$A=1,400\times \frac{(1+0.08{)}^1-1}{0.08}$$ $$A=1,400\times \frac{1.08-1}{0.08}$$ $$A=1,400\times \frac{0.08}{0.08}$$ $$A=1,400\times 1=1,400$$

However, if the question refers to the present value of an annuity (which is more common in such problems), the formula is:

$$PV=P\times \frac{1-(1+r{)}^{-n}}{r}$$

For $n=1$: $$PV=1,400\times \frac{1-(1.08{)}^{-1}}{0.08}$$ $$PV=1,400\times \frac{1-0.9259}{0.08}$$ $$PV=1,400\times \frac{0.0741}{0.08}$$ $$PV=1,400\times 0.92625\approx 1,296.75$$

But since none of the options match, the question likely expects the future value of a single payment (compound interest) for one year:

$$A=P(1+r)=1,400\times 1.08=1,512$$

Thus, the correct answer is Rs. 1,512 (Option b).