For 3 years, the difference between simple interest and compound interest is Rs. 616 at 8% per annum. Find the compound interest in 2 years at the same rate of interest at same sum.
1. Rs. 2240
2. Rs. 4150
3. Rs. 5200
4. Rs. 1250
1. Rs. 2240
2. Rs. 4150
3. Rs. 5200
4. Rs. 1250
Correct Answer – Option 3 : Rs. 5200
Given:
For 3 years, the difference between simple interest and compound interest = Rs. 616
Rate = 8%
For compound interest, time = 2 years.
Concept used:
C.I. = P{(1 + R/100 )T – 1}
D = P × (R/100)2(300 + R)/100
S.I. → Simple interest
P → Principal
T → Time
R → Rate%
C.I. → Compound interest
D → Difference between S.I. and C.I. for 3 years difference,
Calculations:
D = P × (R/100)2(300 + R)/100
⇒ 616 = P × (8/100)2(300 + 8)/100
⇒ 616 = P × (64/10000) × (308/100)
P = (616 × 10000 × 100)/(308 × 64)
⇒ Rs. 31,250
At the same sum,
C.I. = P{(1 + R/100 )T – 1}
⇒ 31250{(1 + 8/100)2 – 1}
⇒ 31250 × {(108/100) × (108/100) – 1}
⇒ 31250 × {(11664/10000) – 1}
⇒ 31250 × (1664/10000)
⇒ Rs. 5200
∴ The compound interest is Rs. 5200