Calculate the Required Deposit for Future Value

B

On the BAII Plus, press 48 N, 5 divide 12 = I/Y, 0 PMT, 4000 FV, CPT PV. On the HP12C, press 48 n, 5 ENTER 12 divide i, 0 PMT, 4000 FV, PV. Make sure the

BAII Plus has the P/Y value set to 1.

To calculate the deposit needed to have $4,000 in 4 years with monthly compounding interest at 5%, we can use the formula for the future value of a lump sum:

FV = PV * (1 + r/n)^(n*t)

Where: FV = Future value ($4,000) PV = Present value (deposit) r = Annual interest rate (5% or 0.05) n = Number of compounding periods per year (12 for monthly compounding) t = Number of years (4)

We need to solve for PV. Rearranging the formula, we have:

PV = FV / [(1 + r/n)^(n*t)]

Substituting the given values, we get:

PV = $4,000 / [(1 + 0.05/12)^(12*4)]

Now let's calculate the value of the expression in the denominator first:

(1 + 0.05/12)^(12*4) = (1 + 0.004167)^48 ≈ 1.218993

Now divide $4,000 by this value:

PV = $4,000 / 1.218993 ≈ $3,276.28

Therefore, the deposit needed today is approximately $3,276.28.

The correct answer is B. $3,276.28.