Answer:
approximately 2.7 years
Step-by-step explanation:
The formula for calculating Compound Interest is
A = P(1 + r/n)^nt
Where P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
A = $55,000
P = $40,000
r = 12% = 0.12
n = 4
We are to look for t = number of years the amount is deposited or borrowed for
55,000 = 40,000 (1 + 0.12/4)^4t
55,000 = 40,000 (1.03)^4t
55,000/40,000 = 1.03^4t
1.375 = 1.03^4t
1.03^10.77 = 1.03^4t
4t = 10.77
t = 10.77/4
t = 2.7 years