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.