A couple needs $55,000 as a down payment for a home. If they invest the $40,000 they have at 12% compounded quarterly, how long will it take for the money to grow to $55,000

approximately 2.7 years

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