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Isabel is shopping for her new car. She identified six models she likes at a local dealership. The table lists the down payment she would need to make on each car to keep the monthly payment within her budget. Assume that she's using only the money accumulated in her savings account to make the down payment. Use this information and the appropriate time value of money formula e to select all the cars that are within Isabel's budget.​

Isabel is shopping for her new car She identified six models she likes at a local dealership The table lists the down payment she would need to make on each car class=

Respuesta :

The amount in Isabel's account after 3 years can be calculated using the

future value of an annuity formula.

The cars within Isabel's budget are;

  • Choice 2
  • Choice 3
  • Choice 4

Reasons:

The amount she saves every month, PMT = $200

The compound interest on the account, r = 1.7%

The value of the account after t = 3 years is given as follows;

[tex]\displaystyle FV = \mathbf{ PMT \cdot \frac{\left( \left( 1 + i \right)^n - 1 \right)}{i}}[/tex]

Where;

[tex]\displaystyle i = \frac{r}{12}[/tex]

n = 12 × t

Which gives;

[tex]\displaystyle FV = 200 \times \frac{\left( \left( 1 + \frac{1.7}{12} \right)^{12 \times 3} - 1 \right)}{\frac{1.7}{12} } \approx \mathbf{7,381.4}[/tex]

Therefore, the cars within her budget for which she can make a down payment are cars that require a down payment of less than $7,381.4, which are;

Choice 2, that requires a down payment of $6,200

Choice 3, that requires a down payment of $5,100

Choice 4, that require a down payment of $7,250

Question parameters obtained from a similar question posted online are;

The amount Isabel saves each month = $200

The compound interest rate on the account = 1.7% compounded monthly

Learn more about the future value of an annuity here:

https://brainly.com/question/4440017

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