Question

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.

Answer 1

2.79 quarters, so almost 3 quarters or 9 months

Step-by-step explanation:

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

`5,470(1+0.048)^(X) = 6,253\\(1.048)^(X)  = (6,253)/(5,470) \\(1.048)^(X) = 1.14\\XLog1.048 = Log 1.14\\X = (Log1.14)/(Log 1.048) \\\\X = 2.79\\`