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You are borrowing N$80,000 for 25 years at 10% nominal annual interest. How much must your annual payments be if you will completely retire the loan over the 25-year period by factor formula

Question

You are borrowing N$80,000 for 25 years at 10% nominal annual interest. How much must your annual payments be if you will completely retire the loan over the 25-year period by factor formula

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Solution

To calculate the annual payments for a loan, you can use the formula for an annuity, which is:

P = [r*PV] / [1 - (1 + r)^-n]

Where: P = annual payment r = interest rate per period PV = present value, or initial amount of the loan n = number of periods

In this case, the interest rate (r) is 10% or 0.10, the present value (PV) is N$80,000, and the number of periods (n) is 25 years.

So, substituting these values into the formula, we get:

P = [0.10 * 80000] / [1 - (1 + 0.10)^-25]

Now, calculate the values in the brackets:

P = 8000 / [1 - (1.10)^-25]

Next, calculate the value of (1.10)^-25:

P = 8000 / [1 - 0.092]

Finally, calculate the annual payment:

P = 8000 / 0.908

P = N$8810.57

So, your annual payments would be approximately N$8810.57 to completely retire the loan over the 25-year period.

This problem has been solved

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