Question

Use the compound interest formula to compute the total amount accumulated and the interest earned $4500 for 3 years at 5% compounded quarterly The total amount accumulated after 3 years is $5223.40 (Round to the nearest cent as needed.) The amount of interest earned is $ (Round to the nearest cent as needed.)

Answer 1

Answer with explanation:

The formula to find the compound amount if compounded quarterly :-

 $A=P(1+\dfrac{r}{4})^{4t}$, where P is the principal amount, r is the rate of interest ( in decimal) and t is the time period ( in years).

Given : P=  $4500 , r= 5%=0.05 and t= 3 years

Then, the compound amount after 3 years if compounded quarterly :-

 $A=4500(1+\dfrac{0.05}{4})^{4(3)}\\\\\Rightarrow\ A=4500(1+0.0125)^{12}\\\\\Rightarrow\ A=4500(1.0125)^{12}\\\\\Rightarrow\ A=4500(1.16075451772)\\\\\Rightarrow\ A=5223.39532974\approx5223.40$

Hence, the total amount accumulated after 3 years is $5223.40

Interest = Compound Amount - Principal amount

=$5223.40-$4500=$723.4

Hence, the  amount of interest earned is $723.4 .