Question : Vipul and Manish invested the sum of INR 15,000 and INR 20,000 at the rate of 20% per annum and 30% per annum respectively on compound interest (compounding annually). If time period is 3 years for both, then what will be the total compound interest earned by Vipul and Manish?
Option 1: INR 32,480
Option 2: INR 31,688
Option 3: INR 29,460
Option 4: INR 34,860
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Correct Answer: INR 34,860
Solution :
Given: Vipul and Manish invested the sum of INR 15,000 and INR 20,000 at the rate of 20% per annum and 30% per annum respectively on compound interest (compounding annually).
We know the formulas,
$A = P(1+\frac{R}{100})^T$
$CI = A-P$
where $CI$, $A$, $P$, and $R$ are the compound interest, amount, principal, and rate.
$CI$ earned by Vipul,
$A = 15000(1+\frac{20}{100})^3$
⇒ $A = 15000(1+0.20)^3$
⇒ $A = 15000\times(1.20)^3$
⇒ $A = 15000\times1.728=$ INR 25,920
$CI = A- P$
⇒ $CI = 25920-15000=$ INR 10,920
$CI$ earned by Manish,
$A = 20000(1+\frac{30}{100})^3$
⇒ $A = 20000(1+0.30)^3$
⇒ $A = 20000\times(1.30)^3$
⇒ $A = 20000\times2.197=$ INR 43,940
$CI = A- P$
⇒ $CI = 43940- 20000=$ INR 23,940
The total compound interest earned by Vipul and Manish = INR 43940 + INR 23940 = INR 34,860.
Hence, the correct answer is INR 34,860.
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