First, let's calculate the maximum loan amount Tyresa can take out for a new car under the advertised rate of 2.79% APR.
Using the formula A = P[(1+ r/n)^(nt) -1], we can plug in the values:
P = $350 (maximum monthly payment)
r = 0.0279 (annual interest rate of 2.79%)
n = 12 (interest is compounded monthly)
t = 4 (4 years)
A = P[(1 + r/n)^(nt) - 1]
A = $350[(1 + 0.0279/12)^(12*4) - 1]
A = $350[(1 + 0.002325)^(48) - 1]
A = $350[(1.002325)^48 - 1]
A = $350[1.12327 - 1]
A = $350[0.12327]
A = $43.1425
Therefore, the maximum loan amount Tyresa can take out for a new car is $43.14.
Now, let's calculate the maximum loan amount for a used car under the advertised rate of 3.29% APR using the same formula.
P = $350 (maximum monthly payment)
r = 0.0329 (annual interest rate of 3.29%)
n = 12 (interest is compounded monthly)
t = 4 (4 years)
A = P[(1 + r/n)^(nt) - 1]
A = $350[(1 + 0.0329/12)^(12*4) - 1]
A = $350[(1 + 0.0027425)^(48) - 1]
A = $350[(1.0027425)^48 - 1]
A = $350[1.14793 - 1]
A = $350[0.14793]
A = $51.7485
Therefore, the maximum loan amount Tyresa can take out for a used car is $51.75.
Financial 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 = P[(1+ ) −1] rn nt rn (1+ ) , where P is the monthly payment, r is the annual interest rate, n is the number times interest is compounded in one year, and t is the number of years. To receive full credit, be sure to show all steps and calculations used, included where you rounded.
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