Question

1. a student is awarded a $1000 scholarship and places it in an account that pays 3% simple interest per year.

a) what is the total value of the scholarship amount at the end of the second year?
b) what is the single percent increase in value of the scholarship after two years?

Explanation:

Step1: Recall simple interest formula

The formula for total amount with simple interest is $A = P(1 + rt)$, where $P$ is principal, $r$ is annual interest rate, $t$ is time in years.

Step2: Define variables for part a

$P = 1000$, $r = 0.03$, $t = 2$

Step3: Calculate total amount (part a)

$A = 1000(1 + 0.03\times2) = 1000(1.06) = 1060$

Step4: Calculate total interest (part b)

Total interest earned: $1060 - 1000 = 60$

Step5: Find percent increase (part b)

Percent increase = $\frac{\text{Interest}}{\text{Principal}} \times 100\% = \frac{60}{1000} \times 100\% = 6\%$

Answer:

a) $\$1060$
b) $6\%$