18 otis has saved $18,500 so far to buy a hou...
18 otis has saved $18,500 so far to buy a house. he can put this amount into an account that earns 5.1% simple interest, or another with 5.1% compounded annually. which method of earning interest should he choose, simple or compound, and how much more interest will the account earn using that method after 4 years? f compound interest; $15,106.30 g simple interest; $15,106.30 h simple interest; $298.65 j compound interest; $298.65
Answer
# Answer:
J. Compound interest; $298.65
# Explanation:
## Step1: Calculate simple - interest
The simple - interest formula is $I = Prt$, where $P=\$18500$, $r = 0.051$ (since $5.1\%=0.051$), and $t = 4$ years.
$I_{s}=18500\times0.051\times4=18500\times0.204 = 3774$
## Step2: Calculate compound - interest
The compound - interest formula is $A=P(1 + r)^{t}$, where $P = 18500$, $r=0.051$, and $t = 4$.
$A=18500\times(1 + 0.051)^{4}=18500\times(1.051)^{4}$
$(1.051)^{4}=1.051\times1.051\times1.051\times1.051\approx1.2199$
$A\approx18500\times1.2199 = 22568.15$
$I_{c}=A - P=22568.15-18500=4074.15$
## Step3: Find the difference
$I_{c}-I_{s}=4074.15 - 3774=298.65$
Since $I_{c}>I_{s}$, compound interest is the better choice.