How much must Harry's Hardware deposit at a 14.5% annual interest for 240 days in order to earn $500 in simple interest?
Would the answer be 547.85?
This is the equation I used.
A = P(1 + rt)
Looks like you used 500 as your principle, P, but 500 is your interest, I.
Use I=Prt
and solve for P.
Yes, the answer is $547.85.
To calculate it, we can use the formula for simple interest:
A = P(1 + rt)
Where:
A is the total amount (initial deposit + interest)
P is the principal (initial deposit)
r is the interest rate (14.5% expressed as a decimal, which is 0.145)
t is the time in years (240 days divided by 365 to convert it to years)
Let's plug in the values:
$500 = P(1 + 0.145 * (240/365))
To solve for P, we can rearrange the formula:
P = $500 / (1 + 0.145 * (240/365))
Calculating it gives us:
P ≈ $547.85
So, Harry's Hardware would need to deposit approximately $547.85 in order to earn $500 in simple interest.
To find out how much Harry's Hardware needs to deposit, we can use the formula for simple interest:
I = Prt
Where:
I is the interest earned, which is given as $500
P is the principal amount (the initial deposit)
r is the interest rate per year, which is given as 14.5% or 0.145
t is the time in years, which is given as 240 days or 240/365 ≈ 0.6575 years
Let's substitute the values into the formula:
500 = P(0.145)(0.6575)
Now we can solve for P:
500 = 0.095525P
Divide both sides of the equation by 0.095525 to isolate P:
P = 500 / 0.095525 ≈ 5230.05
So the amount Harry's Hardware needs to deposit is approximately $5230.05, not $547.85.