Metropolis currently has $1,150,000 in cash. How long would it take them to accumulate $2,000,000 in cash? Assume an interest rate of 5 percent.
To determine how long it would take Metropolis to accumulate $2,000,000 in cash with an interest rate of 5 percent, we can use the concept of compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value (the amount of money Metropolis wants to accumulate, which is $2,000,000)
P = the principal amount (the starting cash balance, which is $1,150,000)
r = the annual interest rate (5 percent or 0.05)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we want to find the number of years, so let's rearrange the formula:
t = (ln(A/P)) / (n * ln(1 + r/n))
Now, we can substitute the given values into the formula:
t = (ln(2,000,000 / 1,150,000)) / (1 * ln(1 + 0.05/1))
Using a calculator, we can solve the equation:
t ≈ (ln(1.7391304)) / (0.05)
t ≈ 2.599 / 0.05
t ≈ 51.98
Therefore, it would take approximately 52 years for Metropolis to accumulate $2,000,000 in cash with an interest rate of 5 percent.