Question

The compound interest of a sum in 8 years is Rs 400 and compound interest of same sum in 16 years become Rs 1300 . Find the compound interest on same sum of money in 20 years.

Answer 1

Topic - Compound Interest

Given:

• Compound interest for 8 years is Rs. 400
• Compound interest for 16 years is Rs. 1300

To find: Compound interest for 20 years.

Solution:

Let the sum be Rs. P and rate of compound interest be r%.

For 8 years,

P (1 + r/100)⁸ - P = 400

or, P {(1 + r/100)⁸ - 1} = 400 .....(i)

For 16 years,

P (1 + r/100)¹⁶ - P = 1300

or, P {(1 + r/100)¹⁶ - 1} = 1300

or, P {(1 + r/100)⁸ + 1} {(1 + r/100)⁸ - 1} = 1300 .....(ii)

Dividing (ii) by (i), we get

(1 + r/100)⁸ + 1 = 13/4

or, (1 + r/100)⁸ = 9/4

or, 1 + r/100 = (9/4)^(1/8)

or, r/100 = (9/4)^(1/8) - 1

or, r = 100 * {(9/4)^(1/8) - 1}

or, r = 10.7 (approximately)

Putting r = 10.7 in (i), we get

P {(1 + 10.7/100)⁸ - 1} = 400

or, P = 318.78

We have found:

• Sum, P = Rs. 318.78
• rate of interest, r = 10.7%

Therefore the compound interest in 20 years will be

= P (1 + r/100)²⁰ - P

= Rs. 318.78 * {(1 + 10.7/100)^20 - 1 }

= Rs. 2115.91

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