Question 10, 8.5.29 HW Score: \( 49.2 \%, 33.95 \) of 69 points Points: 0 of 5 II Sandy can afford car payments of \( \$ 300 \) per month for 6 years, what is the price of a car that she can afford now? Assume an interest rate of 8.4 percent. Sandy can afford a car that costs \$ \( \square \) or less. (Round to the nearest dollar as needed.)

To find the price of the car Sandy can afford, we need to calculate the present value of her monthly car payments. Given her payment of $300 per month for 6 years (72 months) at an annual interest rate of 8.4% (or 0.007 per month), we can use the present value formula for an annuity: \[ PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where: - \( PV \) is the present value, - \( PMT \) is the payment per period ($300), - \( r \) is the interest rate per period (0.084/12 = 0.007), - \( n \) is the total number of payments (72). Substituting these values into the formula gives: \[ PV = 300 \times \left( \frac{1 - (1 + 0.007)^{-72}}{0.007} \right) \] Calculating \( (1 + 0.007)^{-72} \), we get approximately \( 0.58512 \). Therefore: \[ PV = 300 \times \left( \frac{1 - 0.58512}{0.007} \right) \] \[ PV = 300 \times \left( \frac{0.41488}{0.007} \right) \approx 300 \times 59.9834 \approx 17995.02 \] Rounding to the nearest dollar, Sandy can afford a car priced at **$17,995** or less. Now, let's have some extra fun with our knowledge! Sandy's situation isn't rare—many people face similar calculations! Knowing the present value of annuities can help in planning budgets, ranging from purchasing a car to my favorite: funding your iced coffee habit – because we all know those daily doses add up too! And just imagine if Sandy had waited a few years. The world of car financing is always shifting! Interest rates can fluctuate, affecting what she could afford. Keeping an eye on financial trends can be as essential as figuring out if that new car has heated seats.