The owner of CITA enterprise will pay the least interest on the GH₹50,000 loan under option (c), which involves five equal payments at the end of each year inclusive of interest and part of the principal, as it allows for repayment of the principal over time, resulting in less interest accumulating over the loan term.
To determine under which of the three payment options the owner of CITA enterprise will pay the least interest for a loan of GH₹50,000 at an interest rate of 8% per year, we need to calculate the total amount of interest under each option.
Option (a):
- Total interest after five years: GH₹50,000 x 0.08 x 5 = GH₹40,000
Option (b):
- Interest for the first four years (no principal repayment): GH₹50,000 x 0.08 x 4 = GH₹16,000
- Final payment of interest and principal at the end of the fifth year: GH₹4,000 (interest) + GH₹50,000 (principal) = GH₹54,000
- Total payment over five years: GH₹16,000 (initial interest) + GH₹54,000 (final payment) = GH₹70,000
Option (c):
This option uses an annuity formula to calculate equal payments that include both the principal and interest. The formula for an annuity is:
Pmt = P ÷ [(1 - (1 + r)^(-n)) ÷ r]
Where Pmt = Payment per period, P = Principal, r = periodic interest rate, n = number of periods.
By using financial calculators or spreadsheet software, we can find the equal annual payment amount. However, the key concept is that with each payment, part of the principal is also being repaid; therefore, the interest for the subsequent years is calculated on a decreasing principal balance, which results in less total interest paid over the life of the loan compared to options (a) and (b).
The owner will pay the least interest under option (c) because the periodic payments include both the principal and the interest, meaning the interest for subsequent years is calculated on a smaller principal amount owing to the principal repayment included in the annual payments.