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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?

firstly we use the present value annuity formula for this problem as there is future consistent payments that will be done and so we want to evaluate the present value for these two interest rates that are given respectively which is 2.79% and 3.29% which is compounded annually. therefore we will start by calculating the present value for payments on a new car loan.

we are given that she does not want to pay more than $350 per month therefore this gives us the future payments per month of $350 and now we know that the interest rates must be adjusted to monthly compounding so we will use this present value annuity formula:

[tex]Pv = C[(1-(1+i)^n)/i][/tex]

we will substitute values as follows ;

Pv is the present value we are looking for for the new car loan

C is the periodic payments which is the $350 per month she can afford.

i is the interest rate adjusted to monthly rate which is 2.79%/12

n is the number of payments made so 4years x 12 months = 48 months that she will be repaying the loan.

Pv = 350[(1-(1+(2.79%/12))/(2.79%/12)] then compute on calculator.

Pv = $15879.04 this is the maximum amount she can take for a new car loan.

then for the old car loan we only change i from the above interest to 3.29%/12 then substitute all the other values the same to the above mentioned present value formula.

Pv = 350[(1-(1+(3.29%/12))/(3.29%/12)]

Pv= $15721.34 so this is the maximum amount she can take for an old car loan.

lhmarianateixeira lhmarianateixeira · Answer 2 · 2022-02-25T13:37:10+01:00

In this exercise we have to use the knowledge of finance to calculate the value of the cars, as follows:

For the old car we have $15721.34

For the new car we have $15879.04

Organizing the information given in the statement we find that:

new car loans at 2.79% APR
used car loans at 3.29%
72 months.
$350 a month for a maximum of four years

Using the present value formula we find that:

[tex]P_v=C[(1-(1+i)^n/i)][/tex]

Where:

Pv: is the present value we are looking for for the new car loan
C: is the periodic payments
i: is the interest rate adjusted to monthly rate
n: is the number of payments

So the knowing values will be:

For new car:

[tex]P_v = 350[(1-(1+(2.79\%/12))/(2.79\%/12)] \\P_v = \$15879.04[/tex]

For old car:

[tex]P_v = 350[(1-(1+(3.29\%/12))/(3.29\%/12)]\\P_v= \$15721.34[/tex]

See more about finances at brainly.com/question/10024737