Answer :
**A.** To calculate the total amount of interest to be paid, we can use the formula for the total amount of interest paid on a reducing balance loan:
Total interest = Principal * (Interest rate / Compounding frequency) * [(1 + Interest rate / Compounding frequency)^ (Number of payments * Compounding frequency) - 1] / [(1 + Interest rate / Compounding frequency) - 1]
In this case, the principal is K2700, the interest rate is 14% per annum compounded quarterly, the number of payments is 5 * 4 = 20 (since there are 4 quarters in a year), and the compounding frequency is 4 (since the interest is compounded quarterly).
Plugging these values into the formula, we get:
Total interest = 2700 * (0.14 / 4) * [(1 + 0.14 / 4)^ (20 * 4) - 1] / [(1 + 0.14 / 4) - 1]
= 2700 * (0.035) * [(1.035)^ 80 - 1] / [1.035 - 1]
= 2700 * 0.035 * (2.977 - 1) / 0.035
= 2700 * 1.977
= K5344.90
Therefore, the total amount of interest to be paid is K5344.90.
**B.** To calculate the amount of principal paid off in the first three loan repayments, we can use the formula for the principal paid off in a reducing balance loan:
Principal paid off = Installment amount * [1 - (1 + Interest rate / Compounding frequency)^ (-Number of payments * Compounding frequency)] / (Interest rate / Compounding frequency)
In this case, the installment amount is K1899.75, the interest rate is 14% per annum compounded quarterly, the number of payments is 3, and the compounding frequency is 4 (since the interest is compounded quarterly).
Plugging these values into the formula, we get:
Principal paid off = 1899.75 * [1 - (1 + 0.14 / 4)^
Total interest = Principal * (Interest rate / Compounding frequency) * [(1 + Interest rate / Compounding frequency)^ (Number of payments * Compounding frequency) - 1] / [(1 + Interest rate / Compounding frequency) - 1]
In this case, the principal is K2700, the interest rate is 14% per annum compounded quarterly, the number of payments is 5 * 4 = 20 (since there are 4 quarters in a year), and the compounding frequency is 4 (since the interest is compounded quarterly).
Plugging these values into the formula, we get:
Total interest = 2700 * (0.14 / 4) * [(1 + 0.14 / 4)^ (20 * 4) - 1] / [(1 + 0.14 / 4) - 1]
= 2700 * (0.035) * [(1.035)^ 80 - 1] / [1.035 - 1]
= 2700 * 0.035 * (2.977 - 1) / 0.035
= 2700 * 1.977
= K5344.90
Therefore, the total amount of interest to be paid is K5344.90.
**B.** To calculate the amount of principal paid off in the first three loan repayments, we can use the formula for the principal paid off in a reducing balance loan:
Principal paid off = Installment amount * [1 - (1 + Interest rate / Compounding frequency)^ (-Number of payments * Compounding frequency)] / (Interest rate / Compounding frequency)
In this case, the installment amount is K1899.75, the interest rate is 14% per annum compounded quarterly, the number of payments is 3, and the compounding frequency is 4 (since the interest is compounded quarterly).
Plugging these values into the formula, we get:
Principal paid off = 1899.75 * [1 - (1 + 0.14 / 4)^
