Questions :
If the compound interest on a certain sum at 16⅔% per annum for 2 years is ₹2600, find the simple interest on the same sum at the same rate and for the same period.
Options :
- ₹1080
- ₹1000
- ₹1500
- ₹2400
correct answer : d)
Explanation :
Rate of interest,
16⅔% = 50/3%
Compound Interest for 2 years:
CI = P[(1 + R/100)² − 1]
⇒ 2600 = P[(1 + 50/300)² − 1]
⇒ 2600 = P[(7/6)² − 1]
⇒ 2600 = P[(49/36) − 1]
⇒ 2600 = P(13/36)
⇒ P = 2600 × 36 / 13
⇒ P = 7200
Now, Simple Interest:
SI = (P × R × T)/100
⇒ SI = (7200 × (50/3) × 2)/100
⇒ SI = 2400
Therefore, the simple interest on the same sum at the same rate and for the same period is ₹2400.
Hence, the correct answer is option (d) ₹2400. The values ₹1080, ₹1000, and ₹1500 do not satisfy the given compound interest condition and are therefore incorrect.