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?
No calculations needed.
You are earning 12% p.a. vs paying 9% compounded monthly
Take the loan
e.g. Interest payable for the first month on the loan
= 20000(.09/12) = 150
interest earned on fund in first month
= 20000(.12)(1/12) = 200
To determine whether you should take out the loan or use your investment funds, we need to compare the amount of interest charged on the loan with the amount of interest earned from your investment.
Let's calculate the interest charged on the loan first. The loan charges an interest rate of 9% p.a. compounded monthly. To find the interest charged over a year, we need to calculate the annual percentage rate (APR) first.
The APR formula is APR = (1 + r/n)^(n*t) - 1, where r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, r = 9%, n = 12 (compounded monthly), and t = 1 (since we're considering the interest charged over a year).
So, the APR = (1 + 0.09/12)^(12*1) - 1 = 0.0937 or 9.37%.
Now, let's calculate the interest charged on the loan. The formula for compound interest is A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, the principal amount (P) is N$20,000, the interest rate (r) is 9% compounded monthly (0.09/12), n = 12, and t = 1.
So, the interest charged on the loan = A - P = P(1 + r/n)^(n*t) - P = N$20,000(1 + 0.09/12)^(12*1) - N$20,000 = N$1,680.
Next, let's calculate the interest earned from your investment funds. The investment account earns an interest rate of 12% p.a. compounded annually.
We don't need to calculate the APR because there is only one compounding period per year (compounded annually).
The interest earned from the investment funds = P * r = N$20,000 * 0.12 = N$2,400.
Now, we can compare the interest charged on the loan (N$1,680) with the interest earned from the investment funds (N$2,400).
Since the interest earned from the investment funds is greater than the interest charged on the loan, it would be more beneficial for you to use your investment funds rather than taking out the loan to buy the furniture.