- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 2. Calculate the Effective Annual Rate

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**CFA Practice Question**

An investor invests $5000 today for 7 years at an interest rate of 8% compounded quarterly. Which of the following is true?

A. The effective annual interest rate is 8.24 % and the future value of the investment at the end of 7 years is $8,705.12.

B. The effective annual interest rate is 8.24 % and the future value of the investment at the end of 7 years is $8,725.12.

C. The stated nominal annual interest rate is 8.35 % and the future value of the investment at the end of 7 years is $8,705.12.

**Explanation:**Using Texas Instruments BA II PLUS

To work out the future value:

2nd QUIT: 0.00

2nd CLR TVM: 0.00

2nd P/Y: P/Y = previous value

4 ENTER: P/Y = 4.00

2nd QUIT: 0.00

5000 ± PV: PV = - 5,000.00

28 N: N = 28.00

8 I/Y: I/Y = 8.00

CPT FV: FV = 8,705.12

And to find the effective annual interest rate:

2nd QUIT: NOM = previous value

2nd CLR TVM: NOM = 0.00

8 ENTER: NOM = 6.00

DownArrow: EFF = 0.00

DownArrow: C/Y = previous value

4 ENTER: C/Y =4.00

UpArrow: EFF = 0.00

CPT: EFF = 8.24

Using HP 12C

To find future value:

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

28 n: 28.00000000

2 i: 2.00000000

5000 CHS PV: -5,000..000000

g END: - 3,000..000000

FV: 8,705.12

To find effective rate:

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

8 ENTER: 8.00000000

4 n x i: 2.00000000

100 CHS ENTER PV: -100.00000000

FV: -108.2432160

i: 8.24321600

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**User Contributed Comments**
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User |
Comment |
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Jmcb |
Or just remember the formula for EAR...(1.02)^4-1 (since it is quarterly compounded) = .0824 = 8.24% The calculator keystrokes they give seem a bit much... |