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: The total amount accumulated after 3 years is $5223.40

The amount of interest earned is $723.40

Explanation:

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

`A=P(1+(r)/(4))^(4t)`, where P is the present value , r is the rate of interest ( in decimal) and t is time period ( in years).

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

Then, the total amount accumulated will be :-

`A=(4500)(1+(0.05)/(4))^(4(3))\\\\\Rightarrow\ A=(4500)(1+0.0125)^(12)\\\\\Rightarrow\ A=(4500)(1.0125)^(12)\\\\\Rightarrow\ A=(4500)(1.16075451772)=5223.39532974\approx5223.40\ \ \ [\text{Round to the nearest cent}]`

Thus, the total amount accumulated= $5223.40

The amount of interest earned = A-P=$5223.40 -$4500 =$723.40

Hence, the amount of interest earned = $723.40