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Kasturba Kothari
Asked: 2022-11-09T05:09:05+05:30 In:

A loan of Rs. 16,550 has to be paid in three equal installments at compound interest. Calculate the value of annual installment if the rate of interest is 10% per annum.
1. Rs. 6656
2. Rs. 1243
3. Rs. 6655
4. Rs. 1343
5. None of these.

A loan of Rs. 16,550 has to be paid in three equal installments at compound interest. Calculate the value of annual installment if the rate of interest is 10% per annum.
1. Rs. 6656
2. Rs. 1243
3. Rs. 6655
4. Rs. 1343
5. None of these.
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1 Answer

  1. Correct Answer – Option 3 : Rs. 6655

    Given:

    Principal = Rs. 16,550

    Rate = 10% per annum

    Time = 3 years

    Formula used:

    For Installment at CI,

    P = x/{1 + (R/100)} + x/{1 + (R/100)}2 + x/{1 + (R/100)}3 + …

    where,

    P = Money borrowed or Principal.

    x = value of each instalment

    R = Rate (%)

    Calculation:

    Let value of one instalment be x.

    x/{1 + (R/100)} + x/{1 + (R/100)}2 + x/{1 + (R/100)}3 = 16550

    ⇒ x/{1 + 10/100) + x/(1 + 10/100)2 + x/(1 + 10/100)3 = 16550

    ⇒ x/(1 + 1/10) + x/(1 + 1/10)2 + x/(1 + 1/10)3 = 16550

    ⇒ x/(11/10) + x/(11/10)2 + x/(11/10)3 = 16550

    ⇒ 10x/11 + 100x/121 + 1000x/1331 = 16550

    ⇒ (1210x + 1100x + 1000x)/1331 = 16550

    ⇒ 3310x/1331 = 16550

    ⇒ x = Rs. 6655

    ∴ Annual installment is Rs. 6655

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