MATH SOLVE

4 months ago

Q:
# I REALLY NEED HELP!Courtney plans to buy a new car and determines she can budget $400 monthly for six years. Her bank is offering a 7.5% annual interest rate. What is the maximum car loan she can afford to stay within her budget?Use the formula, A = P[(1+r)^n-1]/r(1+r)^n where P is the monthly payment, r is the monthly rate, and n is the number of months.A. $19,873.45B. $21,000.50C. $23,134.61D. $27,425.75Financial institutions often offer lower auto loan rates for new cars than used ones. A local credit union advertises new car loans at 2.79% APR and used car loans at 3.29% both for up to 72 months.Tyresa wants to buy a car but doesn’t want to spend more than $350 a month for a maximum of four years. What is the maximum loan amount she can take out for a new car and a used car using the advertised rates?Use the formula, A = where P [(1+r)^n-1]/r(1+r)^2 is the monthly payment, r is the monthly rate, and n is the number of months. Show all of your steps.

Accepted Solution

A:

Answer: C. $23,134.61 new: $15879.04; used: $15721.34Step-by-step explanation:1. The monthly rate is 1/12 of the annual rate, so r = 0.075/12 = 0.00625. The number of months is 12 times the number of years, so n = 6·12 = 72. Put these numbers into the given formula and evaluate it. A = 400·(1.00625^72 -1)/(0.00625·1.00625^72) . . . . note we added parentheses to your given formula to define the denominator properly = 400·(1.56611743 -1)/(0.00625·1.56611743) = 226.446972/(0.00625·1.56611743) = 226.446972/0.0097882339 = 23,134.61Courtney can afford a car loan of up to $23,134.61.___2. Though loans are available for up to 72 months, Tyresa wants to pay on a loan for only 4 years, or 48 months. The APRs for new and used cars translate to monthly rates of ... new: 0.0279/12 ≈ 0.002325 = r used: 0.0329/12 ≈ 0.0027416667 = rThe same formula can be used with ... new: P = 350, r = 0.002325, n = 48 ⇒ A = 15879.04 used: P = 350, r = 0.0027416667, n = 48 ⇒ A = 15721.34_____Comment on formula evaluationI find it much easier to do the calculation by writing a formula into a graphing calculator or spreadsheet. The tool can do the arithmetic much faster and there are fewer chances for mistakes. It also helps to have the right formula to begin with. If you use the formulas written here, you will get wrong answers. The product of factors to the right of the division symbol (/) needs to be in parentheses. For the second problem, the formula should be the same as for the first problem. (We can't figure where (1+r)^2 came from.)