Question

4

A person wants to have Rs.2 lac annually for 20
years by investing the amount in an annuity
interest rate of 5%. He will have to invest:
a. Rs.24 lac
b. Rs.2492440
c. Rs.2429000
d. Rs.25 lac​

Answer 1

The Present value of investment is Rs 2492442 , option B

Explanation:

Given as :

The future value of investment after 20 years = f = Rs 200000

The Time period = n =20 years

The rate of interest applied = r = 5% = .05

Let The present value of investment = P

Now, From Equation

Present value = Future value × [
`(1 - (1 +r)^(-n))/(r)` ]

or, P = f × [
`(1 - (1 -r)^(-n))/(r)` ]

Or, P = Rs 200000 × [
`(1 - (1 +0.05)^(-20))/(0.05)` ]

Or, P = Rs 200000 ×
`(1-0.376889482)/(.05)`

Or, P = Rs 200000 ×
`(0.623110518)/(0.05)`

Or, P = Rs 200000 × 12.46221036

Or, P = Rs 2492442.072

So, The present value = P = Rs 2492442

Hence, The Present value of investment is Rs 2492442 , option B . Answer