The Number of Annual Compounding Periods Needed for an Investment to Reach a Specific Value

CFA Level I
#1

You are interested in determining how long it will take an investment of €10,000,000 to double in value. The current interest rate is 7 percent compounded annually. How many years will it take €10,000,000 to double to €20,000,000?

So I basicly do:

PV = 10.000.000 // FV = 20.000.000 CHS // r = 7 // and ask my HP12C for N than I get 11

But the answer in the book is 10,24, what is happening? The result looks right to me, how its not 11 in the book?

ps: is the question example 19 in TVM, page 343, can somebody help, please?

#2

The HP 12C doesn’t understand fractional time periods.

Sorry.

#3

You can solve this equation:

FV = PV(1 + r)n

FV / PV = (1 + r)n

ln(FV / PV) = ln[(1 + r)n] = _n_ln(1 + r)

n = ln(FV / PV) / ln(1 + r)

So,

n = ln(2) / ln(1.07) = 0.6931 / 0.0677 = 10.2448

#4

The formula FV = PV(1 + r)n

I would need to know or will be in the CFA exam on a given paper?

Does it matter round up in the test?

#5

You need to know it, though usually you can do this on your calculator.

CFA Institute knows how the calculators work, so I would expect the answer choices to be whole numbers; i.e., they’ll round off the correct answer.

#6

BAII gives me 10.2448 as well. :confused:

#7

If the exam options have 10 and 11 and the exactly answer is actually 10,24,

Should I go with 10 or 11?

I guess 11, right?

Cuz If I went with 10 that wouldn`t be $ 20.000.000 in the FV but less than that…

#8

I’d go with 11.

But I’d be surprised to see those choices on the exam, given that users of the TI would likely round down while the HP will round up.