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%.
Is that paid annually? 4 years
Sra
To calculate how long it would take Metropolis to accumulate $2,000,000 in cash at a 5% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($2,000,000)
P = the initial amount of money ($1,150,000)
r = the interest rate (5%, or 0.05)
n = the number of times interest is compounded per year (we'll assume it's compounded annually)
t = the number of years
Now, let's plug these values into the formula and solve for t:
$2,000,000 = $1,150,000(1 + 0.05/1)^(1t)
Divide both sides of the equation by $1,150,000:
$2,000,000/$1,150,000 = (1 + 0.05/1)^(1t)
1.739 = (1.05)^(1t)
To solve for t, take the natural logarithm (ln) of both sides of the equation:
ln(1.739) = ln((1.05)^(1t))
Using the logarithmic identity ln(a^b) = b * ln(a), the equation becomes:
ln(1.739) = 1t * ln(1.05)
Now, divide both sides by ln(1.05):
ln(1.739) / ln(1.05) = t
Using a calculator, you can find that ln(1.739) / ln(1.05) is approximately 11.87.
Therefore, it would take Metropolis approximately 11.87 years to accumulate $2,000,000 in cash at a 5% interest rate.