you deposit $800 in an account that earns simple interest at an annual rate of 5%. how long must you leave the money in the account to earn $100 in interest?
I = PRN
$100 = 800 x 0.05 x N (I= $100, P= $800, R=5%=0.05)
$100 = 40 x N
Therefore N = 2.5
It will take 2.5 years
Well, it sounds like you're looking to make some extra dough! With an annual interest rate of 5%, you can calculate the time needed to earn $100 in interest using a simple interest formula.
Let's see... $100 divided by 5% gives us $2,000. This means that after $2,000 worth of time, you'll have earned $100 in interest.
Now, since you initially deposited $800 and you want to hit that $2,000 mark, you still need to earn an additional $1,200 ($2,000 - $800).
If we assume that the interest accumulates linearly, you can divide the additional $1,200 by the annual interest rate of 5% to find the time needed. That's $1,200 divided by 5%, which amounts to $24,000!
So, it appears you'll need to leave the money in your account for a whopping $24,000 worth of time to earn $100 in interest. But hey, at least you'll have some quality time with your money, right?
To find out how long you need to leave the money in the account to earn $100 in interest, we can use the formula for simple interest:
Interest = Principal * Rate * Time
In this case, the principal amount is $800, the rate is 5% (or 0.05 in decimal form), and the interest is $100. Plugging these values into the formula, we get:
$100 = $800 * 0.05 * Time
To solve for Time, divide both sides of the equation by ($800 * 0.05):
$100 / ($800 * 0.05) = Time
Simplifying the equation, we have:
Time = $100 / ($800 * 0.05)
Time = $100 / $40
Time = 2.5 years
Therefore, you need to leave the money in the account for 2.5 years to earn $100 in interest.
To calculate the time required to earn a specific amount of interest using simple interest, you can use the formula:
I = P * r * t
where:
I = interest earned
P = principal amount (initial deposit)
r = interest rate per period
t = time in periods
In this case, the interest you want to earn is $100, the principal amount (initial deposit) is $800, and the interest rate is 5% per year. We need to find the time required (t).
Let's substitute the values into the formula:
$100 = $800 * 0.05 * t
Simplifying the equation:
$100 = $40t
Now, solve for t:
t = $100 / $40
t = 2.5
Therefore, you would need to leave the money in the account for 2.5 years to earn $100 in interest.