MATH SOLVE

3 months ago

Q:
# 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%

Accepted Solution

A:

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%.