Calculate Present Value for CFA Level 1 exam question from Test Prep.

D

On the BAII Plus, press 48 N, 5 divide 12 = I/Y, 0 PMT, 2000 FV, CPT PV. On the HP12C, press 48 n, 5 ENTER 12 divide i, 0 PMT, 2000 FV, PV. Make sure the

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

To calculate the deposit needed to have $2,000 in 4 years, we need to use the formula for the future value of a lump sum investment compounded monthly.

The formula is:

FV = PV × (1 + r/n)^(n × t)

Where: FV = Future value PV = Present value (deposit needed) r = Annual interest rate n = Number of compounding periods per year t = Number of years

In this case, the future value (FV) is $2,000, the annual interest rate (r) is 5%, the compounding periods per year (n) is 12 (since it's compounded monthly), and the number of years (t) is 4. We need to solve for the present value (PV).

Plugging in the values into the formula, we have:

$2,000 = PV × (1 + 0.05/12)^(12 × 4)

Let's solve this equation step by step:

Step 1: Calculate the effective interest rate per compounding period: r/n = 0.05/12 = 0.0041667

Step 2: Calculate the number of compounding periods: n × t = 12 × 4 = 48

Step 3: Substitute the values into the formula and solve for PV: $2,000 = PV × (1 + 0.0041667)^48

Step 4: Calculate the bracket term: (1 + 0.0041667)^48 ≈ 1.221924

Step 5: Rearrange the equation and solve for PV: PV = $2,000 / 1.221924 ≈ $1,638.14

Therefore, the deposit needed to have $2,000 in 4 years, assuming the money will earn interest at 5% per year, compounded monthly, is approximately $1,638.14.

The correct answer is D. $1,638.14.