Question

A man borrows 1.5 million naira to buy a car and is charged compound interest at 5% per annum. He repays three hundred thousand naira at the end of each year. How much does he still owe at the end of 3 years to the nearest hundred naira?

a) ₦825,000
b) ₦745,000
c) ₦905,000
d) ₦660,000

Answer 1

After calculating the compound interest annually and subtracting the yearly repayment for 3 years, the man still owes ₦790,700 to the nearest hundred naira, which is not among the given options.

Step-by-step explanation:

To determine how much a man owes on a loan of 1.5 million naira with a compound interest rate of 5% per annum after making annual repayments of 300 thousand naira for 3 years, we need to calculate the compound interest and subtract the repayments made.

Here's a step-by-step solution:

1. Calculate the amount owed after the first year:
   Initial amount = 1,500,000 naira
   Interest for the first year = 1,500,000 * 0.05 = 75,000 naira
   Total after one year = 1,500,000 + 75,000 = 1,575,000 naira
   Repayment made = 300,000 naira
   Amount remaining = 1,575,000 - 300,000 = 1,275,000 naira
   
   
2. Calculate the amount owed after the second year:
   Interest for the second year = 1,275,000 * 0.05 = 63,750 naira
   Total after second year = 1,275,000 + 63,750 = 1,338,750 naira
   Repayment made = 300,000 naira
   Amount remaining = 1,338,750 - 300,000 = 1,038,750 naira
   
   
3. Calculate the amount owed after the third year:
   Interest for the third year = 1,038,750 * 0.05 = 51,937.50 naira
   Total after third year = 1,038,750 + 51,937.50 = 1,090,687.50 naira
   Repayment made = 300,000 naira
   Amount remaining = 1,090,687.50 - 300,000 = 790,687.50 naira
   
   
4. To the nearest hundred, the amount he still owes at the end of 3 years is ₦790,700.

Thus, the correct option is not listed among the choices, as the closest calculation of the debt remaining after 3 years is ₦790,700 to the nearest hundred naira.