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A sum of Rs. 12,000 is to be paid back in two installments. How much is each installment if the interest is compounded annually at 5% per annum?

A sum of Rs. 12,000 is to be paid back in two installments. How much is each installment if the interest is compounded annually at 5% per annum? Correct Answer Rs. 6453.658

Given:

Sum = Rs 12,000

Rate = 5%

No. of installments (CI) = 2

Formula:

E/ (1 + r/100)1 + E/ (1 + r/100)2 = Sum

Installment = E

Calculation:

E/ (1 + 5/100)1 + E/ (1 + 5/100)2 = 12,000

⇒ E/ (105/100)1 + E/ (1 + 105/100)2 = 12,000

⇒ {E/ (105/100)} (1 + 100/105) = 12,000 (E/ (105/100) taken common)

⇒ {100 E/105} × {205/105} = 12,000

⇒ E = Rs. 6,453.658

Alternation solution:

CI Installment = Sum × (100 + R)/100 × (100 + R)/ (100 + R + 100)

= 12,000 × (100 + 5)/100 × (100 + 5)/ (100 + 5 + 100)

= 12,000 × 105/100 × 105/205

= Rs. 6,453.658

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