Question

An annuity immediate is to be paid for some years at 12% p.a. The present value of the annuity is ₹ 10,000 and the accumulated value is ₹ 20,000. Find the amount of each annuity payment

Answer 1

Given, P = ₹ 10,000, r = 12% p.a., A = ₹ 20,000

∴ i = ${\displaystyle \frac{\text{r}}{100}=\frac{12}{100}}$ = 0.12

Now, ${\displaystyle \frac{1}{\text{P}}-\frac{1}{\text{A}}=\frac{\text{i}}{\text{C}}}$

∴ ${\displaystyle \frac{1}{10,000}-\frac{1}{20,000}=\frac{0.12}{\text{C}}}$

∴ ${\displaystyle \frac{2-1}{20,000}=\frac{012}{\text{C}}}$

∴ ${\displaystyle \frac{1}{20,000}=\frac{0.12}{\text{C}}}$

∴ C = (0.12)(20,000)

∴ C = 2,400

∴ The amount of each annuity payment is ₹ 2,400.