Shortcut Trick
Rate = 7.5% = 3/40 → Fractional value = 43/40.
For 2 years, Principal units = (40 × 43) + 402 = 1720 + 1600 = 3320 units.
Instalment units = 432 = 1849 units.
Given 3320 units = ₹9,960 ⇒ 1 unit = ₹3.
Each instalment = 1849 × 3 = ₹5,547.
∴ The correct answer is ₹5,547.
Alternate Method
Given:
Borrowed Sum (P) = ₹9,960
Rate of Interest (R) = 7.5% per annum
Number of instalments (n) = 2
Formula Used:
For Compound Interest instalments, P = x / (1 + R/100) + x / (1 + R/100)2, where x is the value of each instalment.
Calculations:
⇒ 1 + R/100 = 1 + 7.5/100 = 1 + 3/40 = 43/40
⇒ 9960 = x / (43/40) + x / (43/40)2
⇒ 9960 = x × (40/43) + x × (1600/1849)
⇒ 9960 = x [ (40 × 43 + 1600) / 1849 ]
⇒ 9960 = x [ (1720 + 1600) / 1849 ]
⇒ 9960 = x [ 3320 / 1849 ]
⇒ x = (9960 × 1849) / 3320
⇒ x = 3 × 1849
⇒ x = ₹5,547
∴ The correct answer is ₹5,547.
Additional Information
CI Instalment Formula
For 'n' equal annual instalments at rate R% compound interest: P = x [ 1/(1+r) + 1/(1+r)2 + ... + 1/(1+r)n ], where r = R/100.
SI Instalment Formula
For Simple Interest instalments: Amount = n × x + [ x × R × n(n−1) ] / 200, where x is the annual instalment.
Effective Rate of Interest
If interest is compounded half-yearly, the effective annual rate is [ (1 + R/200)2 − 1 ] × 100%.