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

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?

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


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)


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

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?

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.

BAII gives me 10.2448 as well. :confused:

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…

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.