Given the equation A=250(1.1)t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same. What is the approximate new interest rate? Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%

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andromache andromache · Answer 1 · 2020-07-14T06:04:08+02:00

Answer:

[tex]r \approx 2.41\%[/tex]

Step-by-step explanation:

The computation of the approximate new interest rate is shown below:

As we know that there are four quarters in a year so

The new equation is

[tex]A = 250(1 + r)^{4t}[/tex]

Now to determine the value of interest rate,i.e r, so place this to the first equation.

So,

[tex]250(1.1)^{t} = 250(1 + r)^{4t}[/tex]

[tex]1.1^{t} = (1 + r)^{4t}[/tex]

1.1 = (1 + r)^4

[tex]\sqrt[4]{1.1} = 1 + r[/tex]

[tex]r = -1 + \sqrt[4]{1.1}[/tex]

[tex]r \approx 0.0241[/tex]

[tex]r \approx 2.41\%[/tex]

We simply applied the above formula so that the interest rate could come