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%.

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.

It would take 11 years

To determine how long it would take Metropolis to accumulate $2,000,000 in cash, we need to use the concept of compound interest. Compound interest is calculated using the formula:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial cash)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years

In this case, we need to find the time it takes to reach $2,000,000 starting with $1,150,000 at an interest rate of 5% per year.

Let's calculate:

$2,000,000 = $1,150,000(1 + 0.05/n)^(n*t)

Since we don't know the value of n or t, we need to rearrange the formula to isolate t.

Divide both sides by $1,150,000:

2,000,000 / 1,150,000 = (1 + 0.05/n)^(n*t)

Now, let's use some estimation to narrow down the possible values for n.

Since the question does not specify how frequently interest is compounded, we can assume it is compounded annually, which means n = 1. However, we also need to consider other possibilities, such as quarterly (n = 4), monthly (n = 12), or daily (n = 365), depending on the financial institution's policies.

Let's substitute n = 1 into the equation and solve for t:

2,000,000 / 1,150,000 = (1 + 0.05/1)^(1*t)

1.73913 = (1.05)^t

To solve for t, we need to take the logarithm of both sides of the equation using the base 1.05:

log(1.73913) = t * log(1.05)

t = log(1.73913) / log(1.05)
t ≈ 4.96 years

Therefore, it would take approximately 4.96 years for Metropolis to accumulate $2,000,000 in cash, assuming an interest rate of 5% compounded annually.