A=P(1+r)^2
A= interest
P= principle interest
r= interest rate
t= time in years
If $4500 invested at 7% interest compounded annually yeilds $15600, for how many years was the money invested?
It would help if you proofread your questions before you posted them.
Where is "t" in your equation?
People make mistakes. Calm down.
A=P(1+r)^t
A= interest
P= principle interest
r= interest rate
t= time in years
If $4500 invested at 7% interest compounded annually yeilds $15600, for how many years was the money invested?
To find the number of years the money was invested, we need to use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Final amount of money
P = Principal (initial) amount of money
r = Interest rate
n = Number of times the interest is compounded per year
t = Time in years
In this case, we want to find the number of years (t). We know the following information from the problem:
A = $15600
P = $4500
r = 7% (0.07)
Substituting these values in the formula, we have:
$15600 = $4500(1 + 0.07/n)^(n*t)
As the interest is compounded annually, we have n = 1:
$15600 = $4500(1 + 0.07/1)^(1*t)
Simplifying further, we have:
$15600 = $4500(1 + 0.07)^t
Now, we can solve for t by isolating it:
$15600 / $4500 = (1 + 0.07)^t
3.4667 ≈ (1.07)^t
To solve for t, we can take the logarithm (base 10) of both sides:
log(3.4667) ≈ log[(1.07)^t]
Using the logarithmic property log(a^b) = b * log(a):
log(3.4667) ≈ t * log(1.07)
Finally, we can solve for t by dividing both sides by log(1.07):
t ≈ log(3.4667) / log(1.07)
Using a calculator, we can find the approximate value of t. By performing this calculation, we get:
t ≈ 8.0004
Therefore, the money was invested for approximately 8 years.