A sum of Rs. 4,620 is to be paid back in 2 equal annual instalments. How much is each instalment (in Rs.) if the interest is compounded annually at 10% per annum?

Shortcut Trick

Rate of interest = 10% (per annum)

Fraction value = 10% = 1/10

∴ Principal = 10; Interest = 1

So, total installment = 10 + 1 = 11

So, 210 → Rs. 4620

∴ 121 → (4620/210) × 121 = Rs. 2662

∴ The each instalment (in Rs.) is Rs. 2662

Alternate Method

Given:

Total amount = Rs. 4620

Rate of interest = 10%

Total number of installment = 2

Formula used:

Installment = \(\frac{P}{\left(\frac{100}{100+R} \right)+\left(\frac{100}{100+R} \right)^n}\)

Where, P = Total amount; R = Rate of interest; n = Number of installment

Calculation:

Installment = \(\frac{4620}{\left(\frac{100}{100+10} \right)+\left(\frac{100}{100+10} \right)^2}\)

= 4620/[(10/11) + (10/11)²]

= 4620/[(10/11) + (100/121)]

= 4620/(210/121)

= 4620 × (121/210)

= 2662

∴ The each instalment (in Rs.) is Rs. 2662