Answer:
The new interest rate is about 0.1038.
As a percent, this is about 10.4%.
Step-by-step explanation:
We are given:
[tex]\displaystyle A=250(1.1)^t[/tex]
From this, we can determine that the interest rate is compounded annually at 10%.
We want a new equation that keeps A and P but the interest rate is compounded quarterly.
Compound interest is given by:
[tex]\displaystyle A=P(1+\frac{r}{n})^{nt}[/tex]
Since we are compounding quarterly, n = 4. Since the rate is 10%, r = 0.1. P stays at 250. Therefore:
[tex]\displaystyle A=250(1+\frac{0.1}{4})^{4t}[/tex]
Add:
[tex]\displaystyle A=250(1.025)^{4t}[/tex]
Rewrite:
[tex]A=250((1.025)^4)^t[/tex]
So:
[tex]A\approx 250(1.1038)^t[/tex]
Therefore, the approximate new interest rate is 1.1038 - 1 or about 0.1038.
As a percent, this will be 0.1038 or about 10.4%.
