Final answer:
After calculating the balance with compound interest for each year and subtracting the repayments, the man still owes approximately ₦115,166, which does not match any of the provided options.
Step-by-step explanation:
The question involves calculating the remaining balance on a loan after two repayments with compound interest being applied. To solve this, we need to follow the steps of compounding the interest and then subtracting the repayments made at the end of each year.
Initially, the man borrows ₦185,000. After the first year, the compound interest formula will be:
New Balance = Principal × (1 + Rate)Time
After 1 year: ₦185,000 × (1 + 0.06)1 = ₦185,000 × 1.06 = ₦196,100
He then repays ₦45,000, so the new balance after the first repayment is:
₦196,100 - ₦45,000 = ₦151,100
We then apply compound interest again for the second year:
After 2 years: ₦151,100 × (1 + 0.06) = ₦151,100 × 1.06 ≈ ₦160,166
After the second repayment of ₦45,000, the balance is:
₦160,166 - ₦45,000 = ₦115,166
None of the options provided match the correct answer, which is ₦115,166. Therefore, there might be an error in the question or the options given.