You invest $5000 into an account that has a 2.7% annual interest rate and is compounded quarterly. Approximately how long will i

Question

katrin2010 [14]

2 years ago

7

You invest $5000 into an account that has a 2.7% annual interest rate and is compounded quarterly. Approximately how long will i

t take until you have $7,500 in your account?

Mathematics

1 answer:

allsm [11] · Answer 1 · 2022-10-19T06:30:39+03:00

Since the interest is compounded, we will have to use the compound interest formula.

We Weill plug 7500 in for A, because that's the amount of money that we want to have at the end of some amount of time.

5000 will go in for P because that's the starting amount.

2.7% will be converted into a decimal percentage form. You can do this by dividing by 100, which you will get .027, and then plug that in for r, the rate.

Since the interest is compounded quarterly, n = 4.

After a bit of number crunching, you will get to the point where you have to solve for an exponent. You can easily do this by using the natural log ln(). One property of logarithm is that you can take the exponent and place it in front of the log. Now you can divide both sides to separate and solve for t.