1. **State the problem:** Calculate the monthly payment and total interest for a bank loan of $4500 at 10.5% annual interest over 5 years, then compare with the credit card payments. 2. **Formula:** The monthly payment (PMT) formula is: $$\text{PMT} = P \frac{r/n}{1 - (1 + r/n)^{-nt}}$$ where: - $P = 4500$ (principal) - $r = 0.105$ (annual interest rate as decimal) - $n = 12$ (payments per year) - $t = 5$ (years) 3. **Calculate monthly payment:** Calculate $r/n = \frac{0.105}{12} = 0.00875$ Calculate $nt = 12 \times 5 = 60$ Calculate denominator: $$1 - (1 + 0.00875)^{-60} = 1 - (1.00875)^{-60}$$ Calculate $(1.00875)^{-60} = \frac{1}{(1.00875)^{60}} \approx \frac{1}{1.7137} = 0.5837$$ So denominator: $$1 - 0.5837 = 0.4163$$ Calculate numerator: $$4500 \times 0.00875 = 39.375$$ Calculate PMT: $$\text{PMT} = \frac{39.375}{0.4163} \approx 94.56$$ Rounded to nearest dollar: $$95$$ 4. **Compare monthly payments:** Credit card monthly payment = $132$ Difference: $$132 - 95 = 37$$ Since bank loan payment is less, choice A applies: "The monthly payments for the bank loan are approximately 95. This is 37 less than the monthly credit-card payments." 5. **Calculate total interest for bank loan:** Total paid over 5 years: $$95 \times 60 = 5700$$ Total interest: $$5700 - 4500 = 1200$$ Compare with credit card interest $1836$: Difference: $$1836 - 1200 = 636$$ Since bank loan interest is less, choice B applies: "The total interest paid over 5 years for the bank loan is approximately 1200. This is 636 less than the total credit-card interest."