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Find the yearly installment which discharged a debt of Rs.1320 due in 3 years at 10% simple interest?
1. Rs.520
2. Rs. 500
3. Rs.420
4. Rs. 442

1 Answer

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Correct Answer - Option 1 : Rs.520

Given

Debt = Rs.1320

Time = 3 years

rate = 10%

Formula Used

S.I = PRT/100

In simple interest, The interest is not added in the principal amount during the year.

So, the amount paid = Principal amount + simple interest of the 3 years

Calculation∶

Let the annual installment per year be Rs.x .

So, there will be 3x installments in 3 years.

1320 + S.I of 3 years = 3x      (1)

Rate of interest = 10%

Now,

S.I = PRT/100

S.I1 = (1320 × 10 × 1)/100 = 132

Now in 2nd year, the principal remains = (1320 - x )

So, S.I.2 = [(1320 - x ) × 10 × 1]/100 = 132 - x/10

Now, in final year, the principal remains = (1320 - 2x)

S.I3 = [(1320-2x) × 10 × 1]/100 = 132 - 2x/10

From eq. 1,

1320 + 132 + 132 - x/10 + 132 - 2x/10 = 3x

⇒ 17160 - 3x = 30x

⇒ 33x = 17160

⇒ x = Rs. 520

∴ The required annual installment have to pay that will discharged a debt of Rs.1320 is Rs. 520.

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