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A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.

Answer 1

Step-by-step explanation:

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Answer 2

Given data : A sum of money amounts to Rs 6690 after 3 years and to Rs 10,035 after 6 years on compound interest.

To find : Find the sum.

Solution : A/C to given data;

• A (amount) = Rs 6690
• T (time period) = 3 years

and

• A = Rs 10035
• T = 6 years

Let, the sum be Rs P.

Now, we use formula of amount;

➜ A = P * {1 + R/n}^(T)

where,

• P is principal amount
• R is rate of interest
• n is number of times compound in one t
• T is time period
• A is amount

Now,

➜ A = P * {1 + R/n}^(T)

➜ 6690 = P * {1 + R/100}³ ----{1}

Similarly,

➜ A = P * {1 + R/n}^(T)

➜ 10035 = P * {1 + R/100}⁶ ----{2}

Now, divided eq. {2} by eq. {1}

➜ 10035/6690 = P * {1 + R/100}⁶/P * {1 + R/100}³

➜ 3/2 = {1 + R/100}⁶/{1 + R/100}³

➜ {1 + R/100}³ = 3/2 ----{3}

[From eq. {3}], put value of {1 + R/100}³ in eq. {1}

➜ 6690 = P * {1 + R/100}³

➜ 6690 = P * 3/2

➜ P = 6690 * 2/3

➜ P = 13380/3

➜ P = Rs 4460

Answer : Hence, the sum is Rs 4460.

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