using continous compound interest formula to find the indicated value
A= 99000
P= 72466
R= 7.8%
T= ?
Continuous compound interest formula:
A=PeRT
to find t, take log (natural log) on both sides
ln(A)=ln(P)+RT
Solve for T (about 4 years)
R should be written as a fraction (0.078)
To find the value of T using the continuous compound interest formula, we need to use the formula:
A = P * e^(R * T)
Where:
A = Final amount (99000 in this case)
P = Principal amount (72466 in this case)
R = Annual interest rate in decimal form (7.8% = 0.078 in this case)
T = Time in years (which we want to find)
First, let's solve this equation for T. Dividing both sides of the equation by P, we get:
A/P = e^(R * T)
Next, to isolate T, we will take the natural logarithm (ln) of both sides:
ln(A/P) = ln(e^(R * T))
ln(A/P) = R * T * ln(e)
The natural logarithm of e is equal to 1, so the equation simplifies to:
ln(A/P) = R * T
Now, substitute the given values into the equation:
ln(99000/72466) = 0.078 * T
Using a calculator, evaluate the left side of the equation:
ln(99000/72466) ≈ 0.3112
Now, divide both sides of the equation by 0.078:
0.3112 / 0.078 ≈ 3.9872
Therefore, T is approximately 3.9872 years.