Question

Raja aged 40 wishes his wife Rani to have ` 40 lakhs at his death. If his expectation of life

is another 30 years and he starts making equal annual investments commencing now at 3%

compound interest p.a. how much should he invest annually?​

Answer 1

Answer:

Raja should invest annually 81628

Step-by-step explanation:

Raja aged 40 wishes his wife Rani to have ` 40 lakhs at his death

Let say He invest Rs P per Annum

Amount invested in 30 Years = 30P

Amount after 30 Years for 1st Year investment = P (1 + 3/100)³⁰

Amount after 30 Years for 1st Year investment =  P (1 + 3/100)²⁹

Last Year investment Amount = P( 1 + 3/100)¹

Total Amount

P(1.03) + P(1.03)² +..............................................+P(1.03)²⁹ + P(1.03)³⁰

this is an GP

A = P(1.03)   r = 1.03  n = 30

Sum = P(1.03) ( 1.03)³⁰ - 1) /(1.03 - 1)  = 4000000

=>  P(1.03) ( 1.03)³⁰ - 1) = 120000

=> P = 81628

Raja should invest annually 81628

Answer 2

rs.84007

Step-by-step explanation:

n=30

r=3%

future value of annuity regular is given i.e 40lakhs.

formula = a ( (1+i)^n -1 /i)

substitute the values in answer

so,

40,00,000 = a ( (1+0.03)^30 -1 /0.03 )

40,00,000/47.5754 =a

a = rs.84007