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?

## Walmart company estimates that the computer they plan to buy in 18 months will cost $4,200.

# 2 Answers

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.

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?

Compound interest formula:

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

P = principal amount (what we're looking for)

r = annual rate of interest (.0575)

t = number of years the amount is deposited or borrowed for. (18months translate to 1.5 years)

A = amount of money accumulated after n years, including interest. (4200)

n = number of times the interest is compounded per year (12)

4200 = P(1+.0575/12)^(12*1.5)

4200 = P(1.00479167)^18

4200/(1.00479167)^18 = P

4200/1.089854 = P

$3853.73 = P