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प्रश्न
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?
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उत्तर
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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The future amount, A = ₹ 10,00,000
Period, n = 20, r = 5%, (1.025)20 = 1.675
A = `"C"/"I" [(1 + "i")^"n" - 1]`
I = `5/200` = `square` as interest is calculated semi-annually
A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`
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= `"C"/0.025 [1.675 - 1]`
10,00,000 = `("C" xx 0.675)/0.025`
C = ₹ `square`
