Mr. Moleko needs to borrow R16 000. He can get a loan from his uncle at 18% simple interest per annum for 5…

Question

Mr. Moleko needs to borrow R16 000. He can get a loan from his uncle at 18% simple interest per annum for 5 years, or from the bank at 16% compound interest per annum for 5 years. Which loan option is

ScanSolve AI Tutor · Accepted Answer

To determine the best option for Mr. Moleko, we need to calculate the total amount he would have to repay for each loan option.

Option 1: Uncle's loan (Simple Interest)

Identify the given values.
- Principal (P) = R16 000
- Interest Rate (r) = 18% per annum = 0.18
- Time (t) = 5 years
Calculate the simple interest (I).
The formula for simple interest is $I = P \times r \times t$ .
$I = 16000 \times 0.18 \times 5$ $I = 16000 \times 0.90$ $I = 14400$
Calculate the total amount to be repaid (A).
The total amount is the principal plus the interest: $A = P + I$ .
$A = 16000 + 14400$ $A = 30400$
The total amount to be repaid for the uncle's loan is R 30 400.

Option 2: Bank's loan (Compound Interest)
Identify the given values.
- Principal (P) = R16 000
- Interest Rate (i) = 16% per annum = 0.16
- Number of compounding periods (n) = 5 years (compounded annually)
Calculate the total amount to be repaid (A).
The formula for compound interest is $A = P(1 + i)^n$ .
$A = 16000(1 + 0.16)^5$ $A = 16000(1.16)^5$ $A = 16000 \times 2.10034100096$ $A = 33605.45601536$ $A \approx 33605.46$
The total amount to be repaid for the bank's loan is R 33 605,46.

Conclusion
Compare the total amounts for both options.
- Uncle's loan: R 30 400
- Bank's loan: R 33 605,46
Determine the best option.
Mr. Moleko wants to borrow money, so the best option is the one that requires him to repay the least amount.
Since R 30 400 is less than R 33 605,46, the uncle's loan is the better option.

The option that will be best for Mr. Moleko is the uncle's loan.

Mr. Moleko needs to borrow R16 000. He can get a loan from his uncle at 18% simple interest per annum for 5 years, or from the bank at 16% compound interest per annum for 5 years. Which loan option is

Step-by-step solution

Option 1: Uncle's loan (Simple Interest)

Identify the given values.

Calculate the simple interest (I).

Calculate the total amount to be repaid (A).

Option 2: Bank's loan (Compound Interest)

Identify the given values.

Calculate the total amount to be repaid (A).

Conclusion

Compare the total amounts for both options.

Determine the best option.

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