Answer: a) $2812.44; b) $112.44
Step-by-step explanation:
To solve this problem, we will use the compound interest formula. The formula for compound interest is given by:
[tex]A = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
Where:
[tex]A[/tex] is the amount of money accumulated after
[tex]n[/tex] years, including interest.
[tex]P[/tex] is the principal amount (the initial amount of money).
[tex]r[/tex] is the annual interest rate (decimal).
[tex]n[/tex] is the number of times that interest is compounded per year.
[tex]t[/tex] is the time the money is invested for in years.
Given:
P = 2700 dollars
r = 0.0136 (1.36% annual interest rate)
n = 365 (compounded daily)
t = 3 years
a) Substitute the given values into the compound interest formula:
[tex]A = 2700\left(1 + \frac{0.0136}{365}\right)^{365 \times 3}[/tex]
[tex]A = 2700 \times \left(1.00003726027397\right)^{1095}[/tex]
[tex]A = \$2812.44[/tex]
b) The interest earned is the total amount minus the principal:
[tex]$Interest = A - P[/tex]
[tex]\text{Interest} = \$2812.44 - \$2700[/tex]
[tex]$Interest = \$112.44[/tex]