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प्रश्न
Solve the following :
A shopkeeper insures his shop and godown valued at ₹5,00,000 and ₹10,00,000 respectively for 80 % of their values. If the rate of premium is 8 %, find the total annual premium.
उत्तर
Given, Property value of the shop = ₹5,00,000 Property value of the godown = ₹10,00,000
Since shopkeeper insures shop for 80% and godown for 80%,
∴ Policy value of shop = 80% of its property value
= `(80)/(100) xx 5,00,000`
= ₹4,00,000
Policy vale of godown
= 80% of its property value
= `(80)/(100) xx 10,00,000` = ₹8,00,000
Rate of premium is 8% for the shop as well as for godown.
∴ Amount of premium for the shop
= 8% of its policy value
= `(8)/(100) xx 4,00,000` = ₹32,000
∴ Amount of premium for the shop
= 8% of its policy value
= `(8)/(100) xx 8,00,000` = ₹64,000
∴ Total premium = amount of premium for the shop + amount of premium for the godown
= 32,000 + 64,000
= ₹96,000
∴ Total premium payable by the shopkeeper is ` 96,000.
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For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year
∴ 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]`
= `(2000(square))/square [1 - (square)^-4]`
= 50,000`(square)`[1 – 0.8548]
= ₹ 7,550.40
