Financial Math - How to Calculate Loan Repayments and Final Payments (gr. 12 Math)

Welcome to Mathenatic! In this video, we tackle a challenging exam-type question related to financial mathematics. Peter borrows 500,000 Rand from a bank and agrees to repay the loan with monthly payments of 8,000 Rand, starting one month after the loan is granted. The interest rate is set at 18% per annum, compounded monthly. Our goal is to figure out how many payments of 8,000 Rand Peter will make and determine the size of the final payment.

To begin, we use the present value annuity formula to calculate the number of payments (n). The loan value (P) is 500,000 Rand, the monthly payment (X) is 8,000 Rand, and the interest rate is 18% compounded monthly. After plugging these values into the formula and simplifying, we apply logarithms to solve for n. The result shows that Peter will make 186 full payments of 8,000 Rand, with a fractional payment remaining. The final payment will be slightly less than 8,000 Rand.

Next, we calculate the size of this final payment. A common mistake is to simply multiply the decimal portion of the number of payments by 8,000 Rand, but this approach overlooks the interest accrued over the loan period. To determine the final payment correctly, we move all the payments back to the start, essentially treating it like an outstanding balance calculation. By doing so, we account for the interest that accumulates over time. After this process, we find that the final payment is 1,787.32 Rand.

This video provides a detailed and step-by-step solution to this loan repayment problem, explaining the calculations behind both the regular monthly payments and the final payment. If you’re preparing for financial mathematics exams, this is a helpful example of how to work with loans, compound interest, and payments.

The solution makes use of logs and reversing compound interest. This forms part of our revision for Gr. 12 Mathematics, Paper 1 (NSC, CAPS)

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