The Internet

# Comparing Tebogo's Parents' Loan Repayment Options

0 Points

▲ good image

## Ask AI on The Internet

Question: Tebogo's parents decided that since they cannot afford to cover the total cost of R 14 000 needed for the trip to Cape Town. They decided to borrow the remaining balance of R5 425 at Mbibane Bank. The bank offered them the following options. Option 1:. R 5 425 at 9.7 % per , simple interest for 2 years . Option 2: R5 425 at 9.5% per year compounded yearly for 2 years. Tebogo's father said that option 1 will be the better option. Verify with calculations if his statement is valid. (8)

0 Points

Let's evaluate both options using the given interest rates and time period to determine which option is better for Tebogo's parents. ### Option 1: Simple Interest For simple interest, the formula is: $A = P(1 + rt)$ Where: - $$A$$ is the amount after time $$t$$, - $$P$$ is the principal amount ($$R 5 425$$), - $$r$$ is the annual interest rate (expressed as a decimal), and - $$t$$ is the time in years. Given: - $$P = R 5 425$$, - $$r = 9.7\% = 0.097$$, - $$t = 2$$ years. Calculate the amount ($$A$$): $A = 5425 \times (1 + 0.097 \times 2)$ $A = 5425 \times (1 + 0.194)$ $A = 5425 \times 1.194$ $A = 6481.45$ So the total amount to be paid after 2 years with Option 1 is $$R 6 481.45$$. ### Option 2: Compound Interest For compound interest, the formula is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where: - $$A$$ is the amount after time $$t$$, - $$P$$ is the principal amount ($$R 5 425$$), - $$r$$ is the annual interest rate (expressed as a decimal), - $$n$$ is the number of times the interest is compounded per year, and - $$t$$ is the time in years. Given: - $$P = R 5 425$$, - $$r = 9.5\% = 0.095$$, - $$n = 1$$ (compounded yearly), - $$t = 2$$ years. Calculate the amount ($$A$$): $A = 5425 \left(1 + \frac{0.095}{1}\right)^{1 \times 2}$ $A = 5425 \left(1 + 0.095\right)^2$ $A = 5425 \times (1.095)^2$ $A = 5425 \times 1.199025$ $A = 6502.21$ (rounded to the nearest cent) So the total amount to be paid after 2 years with Option 2 is $$R 6 502.21$$. ### Comparison: - Option 1 (Simple Interest): $$R 6 481.45$$ - Option 2 (Compound Interest): $$R 6 502.21$$ Since $$R 6 481.45$$ (Option 1) is less than $$R 6 502.21$$ (Option 2), Tebogo's father is correct in saying that Option 1 is the better option.

Aug. 12, 2024, 6:50 a.m.

0 Points