A company borrows $75 000 from a bank, to be amortised over five years at 8.5% per annum. The annual instalment is:
Question
A company borrows $75 000 from a bank, to be amortised over five years at 8.5% per annum. The annual instalment is:
Solution
To calculate the annual installment, we need to use the formula for an amortizing loan payment:
P = [r*PV] / [1 - (1 + r)^-n]
Where: P = payment r = annual interest rate divided by the number of periods (in this case, it's annual, so we just use the annual rate) PV = present value, or the amount of the loan n = number of periods (in this case, years)
Step 1: Convert the annual interest rate to a decimal: 8.5% = 0.085
Step 2: Substitute the values into the formula:
P = [0.085 * $75,000] / [1 - (1 + 0.085)^-5]
Step 3: Calculate the numerator (the part above the line in the fraction):
0.085 * 6,375
Step 4: Calculate the denominator (the part below the line in the fraction):
1 - (1 + 0.085)^-5 = 1 - (1.085)^-5 = 1 - 0.6806 = 0.3194
Step 5: Divide the numerator by the denominator to find the annual payment:
19,956.57
So, the annual installment the company would have to pay is approximately $19,956.57.
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