If $10,000 is invested in an account at 4.8% annual simple interest, how long will it take for the account balance to grow to $11,200?
I am confused. How do you do this?
I = PRT
1,200 = 10,000 * 0.048 * T
1,200 = 480T
_____ years = T
Thank you
You're welcome.
Where did you get 1,200?
11,200 - 10,000 = 1200 >> interest
Okay, thanks.
To find the time it will take for an account balance to grow to a certain amount with simple interest, we can use the formula:
A = P(1 + rt)
Where:
A = Final account balance
P = Principal amount (initial investment)
r = Annual interest rate (expressed as a decimal)
t = Time (in years)
In this case, we know the following information:
A = $11,200
P = $10,000
r = 4.8% = 0.048 (as a decimal)
We need to solve for t.
Substituting the values into the formula, we get:
$11,200 = $10,000(1 + 0.048t)
Now, let's solve for t:
Divide both sides of the equation by $10,000 to isolate the (1 + 0.048t) term:
$11,200/$10,000 = 1 + 0.048t
Simplify the left side:
1.12 = 1 + 0.048t
Next, subtract 1 from both sides of the equation:
0.12 = 0.048t
Finally, divide both sides of the equation by 0.048 to solve for t:
0.12/0.048 = t
Using a calculator, we find that t is approximately 2.5 years.
Therefore, it will take approximately 2.5 years for the account balance to grow to $11,200 with an annual simple interest rate of 4.8%.