Q. For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to:

250,000 x (1 + .03 / 365)^t = 1,000,000 where t is in days

solving for t and dividing by 30 gives me 562.24249

as a sanity check,

250,000 x (1 + .03 / 365)^(30 x 562.24249) = 1,000,000

maybe the answer given in the solution is wrong, just like the question from Margin Call in another thread.

edit: using 1 month = 30.417 days, the answer becomes 554.53 and agrees with the answer provided. it doesnt seem fair to expect a test taker to know the exact number of days in a month, on average - 30 days is usually the assumed value.

Fair enough - but no one argues that there’s 12 months a year. If you just use the EAR as your I/Y in your calculator, and convert years to months, you should get the answer that is closest to right - i got 554.59 doing this. Didn’t even for one second waste time thinking how many days are in a month.

im the type that avoids using the finance calculator unless i absolutely have to (such as when the problem requires knowing the exact number of days between two arbitrary dates in a year), or if i have to solve for i when calculating an annuity.

having said that, this problem didn’t actually require using the calculator. i was too slow to realize that you can simply divide the number of days in a year (365) by the number of months (12) to get the average number of days in a month (365/12 = 30.416666… - im ignoring the effect of leap years)

If you want to solve for the number of years required, you would use the effective annual rate of 3.0453%; to solve for the number of days required, you would use the effective daily rate of 3.0%/365 = 0.008219%.

They are just two different ways of looking at the problem. The BAII gives the EXACT years required, including any fractional portion!!!

And I think this exact same example has been beaten to death in a few other threads, for example: