Mr. Sharma wants to divide ₹ 1,68,200 between his two sons who are 16 years and 18 years old respectively, in such a way that the sum invested at the rate of 5% p.a compound interest annually will give the same amount to each when they attain the age of 21 years. How much should he divide the sum ?
Compound Interest
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Question

Mr. Sharma wants to divide ₹ 1,68,200 between his two sons who are 16 years and 18 years old respectively, in such a way that the sum invested at the rate of 5% p.a compound interest annually will give the same amount to each when they attain the age of 21 years. How much should he divide the sum ?

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KnowledgeBoat · Accepted Answer

Given:

Total money = ₹1,68,200

Rate = 5% p.a (compound interest)

Younger son = 16 years → will get money after 5 years

Elder son = 18 years → will get money after 3 years

Let the amount to be distributed to younger son be '₹ x' and to elder son to be '₹ y'

∴ x + y = 168200…….(1)

By formula, A = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Amount after 5 years for younger son (at the age of 21),

A = $x\Big(1 + \dfrac{5}{100}\Big)^5$

= x(1 + 0.05)⁵

Amount after 3 years for elder son (at the age of 21),

A = $y\Big(1 + \dfrac{5}{100}\Big)^3$

= y(1 + 0.05)³

Since both will have same amount at age 21:

∴ x(1 + 0.05)⁵ = y (1 + 0.05)³

⇒ x(1.05)² = y

⇒ x × 1.1025 = y…..(2)

Substituting the value of y from equation (2) in equation (1) :

⇒ x + 1.1025x = 168200

⇒ 2.1025x = 168200

⇒ x = $\dfrac{168200}{2.1025}$

⇒ x = 80,000.

Substituting the value of x in equation (1),

⇒ 80,000 + y = 1,68,200

⇒ y = 1,68,200 - 80,000

⇒ y = 88,200.

Hence, sum should be divided as ₹ 80,000 and ₹ 88,200.