Walmart company estimates that the computer they plan to buy in 18 months will cost $4,200. How much money should be deposited now into an account paying 5.75 % interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?
Let's use the equation A = P(1+r/n)nt to solve this problem.
The target value they need to have at the end is A = $4200.
The interest rate of 5.75% means that r = 0.0575.
Monthly compounding means they will compound the interest 12 times per year so n = 12.
The 18 months needed is 1.5 years so t = 1.5.
We need to find P.
Solving the interest equation for P gives
P = A(1+r/n)-nt
Plugging in the values gives P = $4200(1+0.0575/12)-12*1.5 = $3853.73
Note, you must round up:
At P = $3853.72 (rounded down value) they will wind up with $4199.99 and will be a penny short.
At P = $3853.73 (rounded up value) they will wind up with $4200.00, just enough to buy the computer.