Financial Math - How to Calculate Monthly Payments for Savings with Compound Interest

Welcome to Mathenatic! In this video, we’re tackling a financial mathematics problem focused on calculating the number of monthly payments required to reach a savings goal. The scenario involves Anna, who wants to save 300,000 Rand by contributing 4,000 Rand each month into a savings account earning 15% annual interest, compounded monthly.

To solve this, we’ll use the future value annuity formula, which is perfect for situations where you’re saving a fixed amount each month and want to calculate the total accumulated value after a set number of months. In this case, Anna wants to save 300,000 Rand. The monthly payment she makes is 4,000 Rand, and the interest rate is 15% compounded monthly. The goal is to find out how many payments are needed to reach her target.

We begin by plugging the known values into the formula, with F representing the future value (300,000 Rand), X representing the monthly payment (4,000 Rand), and n representing the number of payments, which we need to solve for. The interest rate is 15% annually, compounded monthly, so we adjust this to a monthly rate of 1.25%.

To solve for n, we manipulate the equation by isolating the variable. After simplifying the terms, we end up with an equation that can be solved using logarithms. Using the log function on a calculator, we calculate that n is approximately 53.24, meaning Anna will need to make 54 payments in total to reach her goal.

However, there's an interesting detail to note: If Anna makes only 53 payments, she will come close but still fall short of her target, reaching about 298,000 Rand. To exceed 300,000 Rand, she can either make one additional payment or leave the funds in the account for an extra month without making another contribution. This way, the interest will push the balance above the 300,000 Rand mark.

In conclusion, Anna can either make 54 payments or, alternatively, make 53 payments and allow the balance to grow for an additional month to exceed her target. This demonstrates the power of compound interest and how small adjustments can significantly affect savings over time.

This section of work forms part of our revision set for Grade 12 Mathematics, Paper 1 (NSC, CAPS)

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