Question

1. mr. rodriguez invests $2,000 in a savings plan. the savings account pays an annual interest rate of 5.75% on the amount he put in at the end of each year. a. how much will mr. rodriguez earn if he leaves his money in the savings plan for 10 years?

Explanation:

Step1: Identify the type of interest

This is simple interest because the interest is calculated on the principal amount each year (the problem says "pays an annual interest rate of 5.75% on the amount he put in at the end of each year", implying simple interest where interest is on the principal). The formula for simple interest is $I = P\times r\times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

The annual interest rate is 5.75%, so in decimal form, $r=\frac{5.75}{100}=0.0575$.

Step3: Identify the principal and time

The principal amount $P = \$2000$ and the time $t = 10$ years.

Step4: Calculate the interest

Using the simple interest formula $I = P\times r\times t$, we substitute the values:
$I=2000\times0.0575\times10$
First, calculate $2000\times0.0575 = 115$. Then, $115\times10 = 1150$.

Answer:

Mr. Rodriguez will earn $\$1150$ in interest.