Question

Your uncle the banker offers to lend you $25,000 to start a new business. You will have to make a payment of $7,000 at the end of each of the next 3 years plus a final payment of $10,000 at the end of Year 4. What annual interest rate is built into this loan?

Answer 1

Answer:

Annual interest rate = 6%

Explanation:

Amount of loan = $25,000

The total amount repaid:

($7,000 × 3 years) + ($10,000 balloon payment)

= (7,000 × 3) + (10,000)

21,000 + 10,000 = $31,000

Interest on payment = repayed amount - loaned amoun

Interest on payment = 31,000 - 25,000 = $6,000

Let the total percentage on the loaned amount be x

Therefore we are looking for what percentage rate of the loaned amount ($25,000) will give the interest of $6,000

x % of 25,000 = 6,000

$\frac{x}{100} \times\ 25,000 = 6,000\\\frac{25,000x}{100} = 6,000\\25,000x = 600,000\\x = \frac{600,000}{25,000}\\x = 24$

Therefore the total percentage interest rate = 24%

Annual interest rate = Total interest rate ÷ number of years

Annual interest rate = 24 ÷ 4 = 6%

∴ Annual interest rate = 6%