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Andrew is saving up money for a down payment on a car. He currently has $5470, but knows he can get a loan at a lower interest rate if he can put down $6253. If he invests the $5470 in an account that earns 4.8% annually, compounded quarterly, how long will it take Andrew to accumulate the $6253? Round your answer to two decimal places, if necessary.

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sebastiansierraocm

Answer:

2.79 quarters, so almost 3 quarters or 9 months

Explanation:

We write the equation, and solve it. To solve for x, as x is an exponent, we must use logarithms.

[tex]5,470(1+0.048)^{X} = 6,253\\(1.048)^{X}  = \frac{6,253}{5,470} \\(1.048)^{X} = 1.14\\XLog1.048 = Log 1.14\\X = \frac{Log1.14}{Log 1.048} \\\\X = 2.79\\[/tex]

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