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Question
A 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?
Solution
Given, Policy value = ₹ 1 lakh,
Period of the policy = 20 years
But, the person dies after paying 10 annual premiums.
∴ Nominee will get entire Policy value of ₹ 1,00,000 on account of death.
Also, rate of bonus is ₹ 7 per thousand per annum
∴ Bonus (per year) = `(7)/(1,000) xx 1,00,000`
= ₹ 700
∴ Bonus for 10 years = 700 x 10 = ₹ 7,000
∴ Amount received by his nominee
= Policy value + Bonus
= 1,00,000 + 7,000
= ₹ 1,07,000
∴ Amount received by his nominee is ₹ 1,07,000.
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∴ Rate of interest per quarter = `square/4` = 4
⇒ r = 4%
⇒ i = `square/100 = 4/100` = 0.04
n = Number of quarters
= 4 × 1
= `square`
⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`
⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`
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= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
