Question

Elan Musk need money for his organisation Space X. He borrowed a certain sum of money and agree to pay off by paying $2320 at the end of first year and $4620 at the end of the second year. If the rate of compound interest is 5% per annum, Find the sum borrowed.
1. $ 6400
2. $ 6700
3. $ 4600
4. $ 7600

Answer 1

Correct Answer - Option 1 : $ 6400

Given∶

He agree to pay $2320 at the end of first year and $4620 at the end of second year.

Rate = 5%

Formula Used∶

A = P(1 + R/100)ⁿ

Calculation∶

Let the money borrowed be $x

Amount after one year = x (1 + 5/100) = $21x/20

Money refunded at the end of first year = $2320

Principal for 2nd year =[(21x/20) - 2320]

Amount at the end of 2nd year = [(21x/20) - 2320] ×  [1 + 5/100]

⇒ [(21x/20) - 2320] × (21/20)

But the money paid at the end of the 2nd year = $4620

[(21x/20) - 2320] × (21/20) = 4620

⇒ (21x/20) - 2320 = (4620 × 20)/21 = 4400

⇒ 21x/20 = 4400 + 2320 = 6720

⇒ x = (6720 × 20) /21 = 320 × 20

⇒ 6400

∴ Elan Musk borrows $6400 for his organisation Space X.