Question

a bank offers a savings account with a yearly simple interest rate of 2%. suppose you deposit $550 into a savings account. how much simple interest do you earn in 4 years? in 4 years and 6 months? show your work.

Explanation:

Step1: Recall simple interest formula

The simple interest formula is $I = P \times r \times t$, where $P$ = principal amount, $r$ = annual interest rate (decimal), $t$ = time in years.

Step2: Define given values

$P = \$550$, $r = 2\% = 0.02$

Step3: Calculate interest for 4 years

Substitute $t=4$ into the formula:
$I = 550 \times 0.02 \times 4$
$I = 550 \times 0.08 = 44$

Step4: Convert 6 months to years

6 months = $\frac{6}{12} = 0.5$ years, so total $t=4.5$ years

Step5: Calculate interest for 4.5 years

Substitute $t=4.5$ into the formula:
$I = 550 \times 0.02 \times 4.5$
$I = 550 \times 0.09 = 49.5$

Answer:

Interest earned in 4 years: $\$44$
Interest earned in 4 years and 6 months: $\$49.50$