Find the amount of an immediate annuity of Rs. 700 a year for 4 years at 5% p.a.

An immediate annuity is a series of equal payments made at the end of each period for a fixed number of years. The present value (PV) of an annuity is calculated using the formula:

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

Where:

• $P$ = Annual payment (Rs. 700)
• $r$ = Annual interest rate (5% or 0.05)
• $n$ = Number of years (4)

Step-by-Step Calculation:

1. Identify the given values:

   • $P=700$
   • $r=0.05$
   • $n=4$

2. Calculate the discount factor: $$\frac{1-(1+r{)}^{-n}}{r}=\frac{1-(1+0.05{)}^{-4}}{0.05}$$

3. Compute $(1+0.05{)}^{-4}$: $$(1.05{)}^{-4}=\frac{1}{(1.05{)}^4}$$ $$(1.05{)}^4=1.21550625$$ $$(1.05{)}^{-4}=\frac{1}{1.21550625}\approx 0.8227$$

4. Substitute back into the discount factor: $$\frac{1-0.8227}{0.05}=\frac{0.1773}{0.05}=3.546$$

5. Calculate the present value (PV) of the annuity: $$PV=700\times 3.546=2482.20$$

Final Answer:

The present value (amount) of the immediate annuity is Rs. 2,482.20.