Question

A man borrows R10000 with interest at 3.5% p.a. the debt is to be retired by the payment of R2 500 at the end of 4 years followed by 6 equal annual payments. Find the outstanding principal just after the 3 rd periodic payment

Answer 1

Step-by-step explanation:

To solve this problem, we need to first calculate the present value of the 6 equal annual payments. We can use the formula for the present value of an annuity to do this:

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

Where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of periods.

Using this formula with the given values, we get:

PV = 2500 * [(1 - (1 + 0.035)^-6) / 0.035] = 12,758.61

So the present value of the 6 equal annual payments is R12,758.61.

Next, we need to calculate the outstanding principal just after the 3rd periodic payment. To do this, we can use the formula for the future value of an annuity:

FV = PMT * [(1 + r)^n - 1 / r]

Where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of periods.

Using this formula with the given values, we get:

FV = 2500 * [(1 + 0.035)^3 - 1 / 0.035] = 8,989.11

So the outstanding principal just after the 3rd periodic payment is:

R10,000 - R8,989.11 = R1,010.89