A new tax business, Taxes Done Right, will purchase a copying machine. After speaking with their financial advisor, they find that the copying machine will cost them $3,300 in 3 years. The account they will invest in earns 5% per year compounded semi-annually. In order to pay cash for the machine, how much should they deposit semi-annually in this account for 3 years?

Answer: $2,845.57965

The principal to be deposited semiannually would be $2,845.58 (rounded to 2 decimal places)

Explanation:

Using compound formula below

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

A = amount = $3,300

r = rate = 5% = 5/100 = 0.05

n = number of compounding rate (semiannually) = 2 interest payments a year

t = time in years = 3

3,300 = p (1 + 0.05/2) ^2 (3)

3,300 = p (1 + 0.025) ^6

3,300 = p (1.025) ^6

3,300 = 1.15969342p

Divide both sided by 1.15969342

p = $ (3,300/1.15969342)

p = $2,845.57965

p ≈$2,845.58 rounded to 2 decimal places.