Question

Sonam wants to buy a car which is worth Rs.76,51,000 and decided to pay in 3 equal instalments but the showroom charges the rate of interest 2% at compound interest. What is the extra amount she will pay over the MRP?
1. 308060
2. 308000
3. 305060
4. 307000
5. 307060

Answer 1

Correct Answer - Option 1 : 308060

Given:

Principal = Rs.76,51,000

Time = 3 years

Rate of interest = 2%

Formula Used:

P × {1 + (R/100)}ⁿ = I × {1 + (R/100)}^{n - 1} + I × {1 + (R/100)}^{n – 2} ………. + I

Where p = principle

n = Time

R = rate percentage at compound interest

I = each instalment

Calculation:

P × {1 + (R/100)}ⁿ = I × {1 + (R/100)}^{n - 1} + I × {1 + (R/100)}^{n – 2} ………. + I

⇒ 7651000 × {1 + (2/100)}³ = I × {1 + (2/100)}² + I × {1 + (2/100)} + I

⇒ 7651000 × (51/50)³ = I × (51/50)² + I × (51/50) + I

⇒ 7651000 × (51/50)³ = I × (2601/2500) + I × (51/50) + I

⇒ 7651000 × (51/50)³ = I × {(2601/2500) + (51/50) + 1}

⇒ 7651000 × (51/50)³ = I × {(2601/2500) + (51/50) + 1}

⇒ 7651000 × (51/50)³ = I × {(2601 + 2550 + 2500)/2500}

⇒ 7651000 × (51/50)³ = I × (7651/2500)

⇒ I = 7651000  × (51/50) × (51/50) × (51/50) × (2500/7651)

⇒ I = (1000 × 51 × 51 × 51)/50

⇒ I = 2653020

Now she pays 3 instalment of Rs.2653020

Total amount paid = 3 × 2653020 = 7959060

Extra amount paid = total amount – MRP

⇒ 7959060 – 7651000 = 308060

∴ The extra amount paid is Rs.308060