1. **State the problem:** Calculate the monthly payment for a used car loan with the following details: - Purchase price: 4235 - Down payment: 85 - Number of monthly payments: 60 - Amount financed: 4150 - APR: 15.5% 2. **Using the table lookup method:** The loan amortization table at 15.5% APR for 60 months gives a monthly payment factor. From the problem, the total of monthly payments is 5984.00, so monthly payment by table is: $$\text{Monthly Payment} = \frac{5984.00}{60} = 99.73$$ 3. **Using the formula method:** The formula for monthly payment $M$ is: $$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$ where: - $P = 4150$ (amount financed) - $r = \frac{15.5}{100 \times 12} = 0.0129167$ (monthly interest rate) - $n = 60$ (number of payments) 4. **Calculate $(1+r)^n$:** $$ (1 + 0.0129167)^{60} = 1.0129167^{60} \approx 2.117$$ 5. **Calculate numerator and denominator:** $$\text{Numerator} = 0.0129167 \times 2.117 = 0.02734$$ $$\text{Denominator} = 2.117 - 1 = 1.117$$ 6. **Calculate fraction:** $$\frac{0.02734}{1.117} \approx 0.02448$$ 7. **Calculate monthly payment:** $$M = 4150 \times 0.02448 = 101.59$$ 8. **Summary:** - Monthly payment by table lookup: $99.73$ - Monthly payment by formula: $101.59$ Both answers are close, with slight differences due to rounding in the table.