# For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily

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:

EAR = (1 + Periodic interest rate)m – 1 EAR = (1 + 0.03/365)365 – 1 EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%.

After that I choose that EAR as my i

set 250K CHS as PV

set 1M as FV

set PMT as 0

got N = 47

47*12 = 564

The right answer is A through, can someone help me?

What calculator are you using?

In any case, why switch it to annual, then monthly?

Use the daily rate and let the calculator tell you how many days it takes. Then convert that to months.

A hp12c

If I calculate the EAR monthly I´m still getting the same number 47 in the end

Also I did what you said:

3/365 i

250K CHS PV

1M FV

0 pmt

16868 days / 30 = 562

Still got the same im actually getting the same answer.

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.

There are more than 30 days in an average month.

Divide by 365.25, then multiply by 12.

Now It`s right… such a very tricky question through…

Why 365,25 thorugh? shouldn`t be 365?

Leap years. 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)

I have one final question for this problem…

I should be getting the n in years = 46,21369863

but when I calculate ear (which I calculated right) and put the 250K CHS PV 1M FV 0 PMT

I get 47 instead of 46,21369863

The EAR I got is: 3,045326360

Can someone explain why the calcualtor gives me 47?

That’s a quirk of the HP12C: it rounds n up to the nearest integer.

That’s why I had asked which calculator you were using; the BA-II doesn’t round n.

That`s terrible, this question is indeed to tricky the candidate (that uses a hp12c) them as a answer they even have what I would get with 47 N

Another reason to do it based on days, not years.

How can I do it based on days, not years?

let`s say I calculated EAR = 3,045326360

I have PV = 250K CHS

FV = 1M

PMT = 0

I ask my calculator and it gives me 47 N

How can I get it in days?

How would you solve this question to make the calculator return in days?

Don’t calculate the EAR, calculate the E_ D _R: the effective _ daily _ rate.

It has the advantage of being very, very easy.