You want to buy furniture which will cost N$ 20,000. You could take out a personal loan
for N$20,000, which would charge you 9% p.a. interest compounded monthly. You also
have N$20,000 in an investment account, where you earn interest of 12% p.a. compounded
annually. Taking account of the interest charged versus interest earned, should you take
out the loan or make use of your investment funds?
To determine whether it is more beneficial to take out the loan or use the investment funds, we need to compare the interest charged on the loan to the interest earned on the investment account.
First, let's calculate the interest charged on the loan over a period of one year. The loan has an interest rate of 9% per annum compounded monthly. To find the effective annual interest rate, we need to account for compounding. The formula to calculate the effective annual interest rate is:
Effective Annual Interest Rate = (1 + (nominal interest rate / number of compounding periods))^(number of compounding periods) - 1
In this case, the nominal interest rate is 9% p.a. and the number of compounding periods is 12 (monthly compounding). Plugging these values into the formula, we get:
Effective Annual Interest Rate = (1 + (0.09 / 12))^(12) - 1
= (1.0075)^(12) - 1
≈ 9.38%
Therefore, the loan would charge you an effective annual interest rate of approximately 9.38%.
Now, let's calculate the interest earned on the investment account over a period of one year. The investment account has an interest rate of 12% per annum compounded annually. So, the interest earned on this account is simply 12% of the principal amount.
Interest Earned on Investment = (12 / 100) * N$20,000
= N$2,400
Comparing the interest charged on the loan (N$20,000 * 9.38% ≈ N$1,876) to the interest earned on the investment (N$2,400), we can see that the interest earned on the investment is greater.
Therefore, it would be more beneficial to use your investment funds of N$20,000 to make the purchase, as the interest earned on the investment exceeds the interest charged on the loan.