CFA® Level 1 Exam Question: Future Value Calculation

Calculating Future Value: CFA® Level 1 Exam Preparation

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Question

How much must you deposit today if you wish to have $60,000 in 10 years, assuming that interest accumulates at 10%, compounded annually?

Answers

Explanations

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A. B. C. D. E.

E

On the BAII Plus, press 10 N, 10 I/Y, 0 PMT, 60000 FV, CPT PV. On the HP12C, press 10 n, 10 i, 0 PMT, 60000 FV, PV. Note that the answer is displayed as a negative number.

To calculate the amount you need to deposit today, you can use the formula for the future value of a lump sum investment:

FV=PV×(1+r)nFV = PV \times (1 + r)^n

Where: FV = Future Value ($60,000 in this case) PV = Present Value (the amount you need to deposit today) r = Interest rate per period (10% in this case) n = Number of periods (10 years in this case)

Now, let's plug in the given values and solve for PV:

60,000=PV×(1+0.10)1060,000 = PV \times (1 + 0.10)^{10}

Simplifying the equation, we have:

60,000=PV×1.101060,000 = PV \times 1.10^{10}

To isolate PV, we divide both sides of the equation by 1.10101.10^{10}:

60,0001.1010=PV\frac{60,000}{1.10^{10}} = PV

Using a calculator, we find:

60,0001.1010≈20,153.37\frac{60,000}{1.10^{10}} \approx 20,153.37

Therefore, the correct answer is option A: $20,153.37.

You need to deposit approximately $20,153.37 today in order to accumulate $60,000 in 10 years, assuming an annual interest rate of 10% compounded annually.

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