how much more interest is earned on an investment of $12,585 at 3.5% interest over 5 years if the interest…

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. Given $P=$12585$, $r = 0.035$ (since $3.5%=0.035$), and $t = 5$ years. $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 the money is invested for. $A = 12585\times(1 + 0.035)^{5}$ $A=12585\times(1.035)^{5}$ $(1.035)^{5}=1.035\times1.035\times1.035\times1.035\times1.035\approx1.187686$ $A = 12585\times1.187686\approx14934.525$ $I_{c}=A - P=14934.525-12585=$2349.525$

Step3: Find the difference

Find the difference between compound - interest and simple - interest: $I_{c}-I_{s}=2349.525 - 2192.875=$156.65$ (There might be a small rounding difference in the official answer. The closest value is considered).

Answer:

B. $$159.65$