Question

Suppose that $590 is deposited into an account that pays 3.5% compounded quarterly. How long will it

will take for the account to contain at least $800? Round to the nearest year.

Answer 1

Answer: 9 years

Explanation:

Let 's use the compound interest formula :

`\rm \displaystyle S=A\left( 1+(N)/(100) \right)^(\rm \big r)`

Where N- the percentage by which we raise the price ; r-years ; A-the original price

In our case

N=3,5% ; r=? ; A=590$

And we know :

`\rm \displaystyle S= 800 \\\\ 590 \left( 1+ (3,5)/(100) \right)^{\big {r}}=800 \\\\\\(1,035)^(\big r) = (80)/(59)\approx1,355 \\\\\\ r= \log_(1,035)\ 1,355=8,\underline831 \approx9 \ years`