- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 1. The Time Value of Money
- Subject 5. The Future Value and Present Value of a Single Cash Flow

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**CFA Practice Question**

What is the minimum number of years required for $1,000 invested at 7% per annum to exceed $1,200 invested at 6% per annum?

A. 15

B. 17

C. 20

**Explanation:**If you use your calculator, you will have to calculate this by trial and error. Choose an arbitrary value for N, and work out the future value for both investments. If there is a discrepancy between the two values, you will have to amend your estimate. Let us choose N = 10.

Using Texas Instruments BA II Plus:

1st Investment

1000 ± PV: 1,000.00

10 N: N = 10.00

7 I/Y: I/Y= 7.00

CPT FV: FV = 1967.15

2nd Investment

1200 ± PV: 1,200.00

10 N: N = 10.00

6 I/Y: I/Y= 6.00

CPT FV: FV = 2149.02

The first investment is slower to increase. Try N=15 and see what happens. Continue until you hit upon the correct value = 20.

Using Hewlett Packard hp 12 C:

Investment 1:

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

10 n: -10.00000000

7 i: 7.00000000

1000 CHS PV: -1,000.000000

g END: -1,000.000000

FV: 1967,151357

Investment 2:

f CLEAR FIN: 0.00000000

f CLEAR REG: 0.00000000

10 n: -10.00000000

6 i: 6.00000000

1200 CHS PV: -1,200.000000

g END: -1,200.000000

FV: 2,149.017236

The first investment is slower to increase. Try N=15 and see what happens. Continue until you hit upon the correct value = 20.

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**User Contributed Comments**
12

User |
Comment |
---|---|

PedroEdmundo |
I didn't get the right answer because of the stress but u can find the right result quicker if u do: 1000*(1.07)^n=1200*(1.06)^n Thus, n=ln(6/5)/ln(1.07/1.06)=19.42 |

sonderfall |
n=(ln 1000 - ln 1200)/(ln 1.06 - ln 1.07) Do not divide but subtract! |

bahodir |
In TI how to find LOG base N? |

TammTamm |
I totally couldn't figure this one out so I just guessed. Of course my guess was incorrect. Thanks sonderfall for the explanation |

Drzewes |
You take: 1000*(1.07)^n=1200*(1.06)^n Divide one by the other and get: 5/6*(1.07/1.o6)^n=1 now for a calculator: PV=-5/6 i=1,07/1,06 FV=1 cmpt for n. You get n=19 which is when these are equal, so you need to add one year, so that the first investment opportunity is bigger. |

migena |
Thanks Drzewes, very insightful your explanation!! |

Criticull |
taking ln is not hard, but it's easier on scientific calculators where you can see what you're typing in. These calculators kinda suck imo. |

azramirza |
The most easy way is equate for both from options a,b and c...and put n in ur calc and find fv... |

dream007 |
Or u can just do trial and error... after all, the answer is bound to be A,B or C. |

akirchner1 |
If doing trial by error, start with B first. You should be able to figure out the right answer based on that. |

rjdelong |
yes I just started with 17 and saw which one was bigger |

farhan92 |
the problem with doing questions after work is i got the answer as 15 but selected 20 -.- off to Arkham i think! |