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Mickey & Minnie have $49 million in cash. Before they retire, they want the $49 million to grow to $90 million. How many years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash? Assume annual compounding. (Enter your answer in years to 2 decimal places, e.g., 12.34)

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6 votes

Answer: 6.68

Preliminary Problem-Solving

To calculate the number of years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash, we can use the formula for compound interest.

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

where

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time in years

Given:

P = $49 million

r = 10.5%

n = 1 (annual compounding)

A = $90 million

Problem-Solving

We need to find t. Let's plug in the given values in the formula and solve for t.

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

90 = 49(1 + 0.105/1) ^ t

Dividing both sides by 49, we get:

1.8367 = (1 + 0.105) ^ t

Taking the logarithm of both sides, we get:

t log (1.105) = log (1.8367)

Dividing both sides by log (1.105), we get:

t = log (1.8367) / log (1.105)

Using a calculator, we get:

t ≈ 6.68

Therefore, it will take approximately 6.68 years before Mickey & Minnie can retire if they earn 10.5% per annum on their stash of cash.

User Nathan Fraenkel
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