Question

Raman borrows a sum of Rs. 30,000 at 25 percent p.a. simple interest, and then lends it to Raghav at 40 percent p.a. compound interest, compounded half-yearly. What will be the gain/loss of Raman after one year?
1. Rs. 6,300
2. Rs. 7,200
3. Rs. 4,500
4. Rs. 5,700

Answer 1

Correct Answer - Option 4 : Rs. 5,700

Given:

Raman borrowed Rs. 30,000 at 25% p.a simple interest

Lend to Raghav at 40% p.a compounded half yearly

Formula used:

S.I = (PRT)/100

C.I = P{(1 + R/100)ⁿ - 1}

Gain= Interest paid by Raman - Interest receive by Raman/Paid by Raghav

Calculation:

 40% p.a compounded half yearly

⇒ Rate for 6 months is 20%

By using the formula of S.I

Total interest paid by Raman = (PRT)/100

⇒ (30,000 × 25 × 1)/100 = 7,500

Total interest received by Raman/Paid by Raghav = P{(1 + R/100)n - 1}

⇒ 30,000{(1 + 20/100)² - 1}

⇒ 30,000{(120/100)² - 1}

⇒ 30,000{(144/100) -1}

⇒ 300(144 - 100)

⇒ 300 × 44 

⇒ 13,200

According to the formula 

Gain = 13,200 - 7,500 = 5,700

∴ Gain of Raman after one year is 5,700.