Calculate the length of time for 800,000to earn 15,000 if invested at 10 percent per annum.
solve either
800,000*0.1t = 15000
or
800,000(1.1^t - 1) = 15000
Calculate the lenght of time
answer
To calculate the length of time it takes for an investment to reach a certain amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case 15,000)
P = the principal amount (in this case 800,000)
r = annual interest rate (in this case 10% or 0.10)
n = number of times interest is compounded per year (assuming annually, so n = 1)
t = number of years
In this case, we need to solve for t. So, our equation becomes:
15,000 = 800,000(1 + 0.10/1)^(1*t)
Simplifying this equation:
15,000/800,000 = (1.10)^t
0.01875 = 1.10^t
To solve for t, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) for this example:
ln(0.01875) = ln(1.10^t)
Now, we can bring down the exponent using the logarithmic property of ln:
ln(0.01875) = t * ln(1.10)
Using a scientific calculator or an online calculator, we can find the natural logarithm of 0.01875, which is approximately -3.979:
-3.979 = t * ln(1.10)
Next, we can divide both sides of the equation by ln(1.10):
-3.979 / ln(1.10) = t
Using a calculator, we can find the value of the right side of the equation, which is approximately -36.541:
t ≈ -3.979 / ln(1.10) ≈ -36.541
The calculated value for t is approximately -36.541. However, since time cannot be negative, we can round up to the nearest whole number:
t ≈ 37 years
Therefore, it would take around 37 years for the investment of 800,000 to earn 15,000 at an interest rate of 10% per annum.