how much more interest is earned on an invest...
how much more interest is earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded annually rather than earning simple interest? a. they are the same. b. $159.65 c. $2,362.03 d. $12,744.65 please select the best answer from the choices provided
Answer
# Answer:
B. $159.65
# Explanation:
## Step1: Calculate simple - interest
The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.
$P=\$12585$, $r = 0.035$, $t = 5$.
$I_{s}=Prt=12585\times0.035\times5=\$2192.875$
## Step2: Calculate compound - interest
The compound - interest formula is $A = P(1 + r)^{t}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.
$A = 12585\times(1 + 0.035)^{5}=12585\times(1.035)^{5}$.
$(1.035)^{5}=1.035\times1.035\times1.035\times1.035\times1.035\approx1.187686$.
$A = 12585\times1.187686\approx14937.55$.
$I_{c}=A - P=14937.55−12585=\$2352.55$
## Step3: Find the difference
$I_{c}-I_{s}=2352.55 - 2192.875=\$159.675\approx\$159.65$