A woman borrowed ₹25,220 and she returned the money in three equal instalments after one, two and three years. If the rate of compound interest is 5%, then find the value of each instalment.

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  1. ₹9,261
  2. ₹8,000
  3. ₹9,000
  4. ₹8,261

Answer (Detailed Solution Below)

Option 1 : ₹9,261
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Detailed Solution

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Given:

Principal = ₹25,220

Rate of interest = 5%

Number of instalments = 3

Formula used:

The present value of the instalments can be found using the formula for compound interest and equal instalments:

P = A/(1 + r)1 + A/(1 + r)2 + A/(1 + r)3

Calculation:

⇒ 25,220 = A/(1.05) + A/(1.05)2 + A/(1.05)3

⇒ 25,220 = A × [1/(1.05) + 1/(1.05)2 + 1/(1.05)3]

⇒ 25,220 = A × [0.9524 + 0.9070 + 0.8638]

⇒ 25,220 = A × 2.7232

⇒ A = 25,220 / 2.7232

⇒ A = ₹9,261

∴ The value of each instalment is ₹9,261.

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