An investment of €500,000 today that grows to €800,000 after six years has a stated annual interest rate closest to:

[ImBruces]

1. 7.5% compounded continuously.
2. 7.7% compounded daily.
3. 8.0% compounded semiannually.

I got stated annual rate as 0,081483747

after applying EAR formula I`m getting higher values through, can somebody help?

[S2000magician]

Your EAR is correct.

How are you converting that to a continuous rate, a stated rate compounded daily, and a stated rate compounded semiannually?

[ImBruces]

I`m doing

EAR = (1+0,081483747/365)³⁶⁵ than -1 and multiply by 100, got 8,48 for daily lol

[S2000magician]

One down, two to go.

[ImBruces]

For semi I got 0,083143648

for continuous got 0,084370898

non of them are the answers…

[S2000magician]

@ImBruces

For semi I got 0,083143648

for continuous got 0,084370898

non of them are the answers…

I didn’t ask what you got; I asked how you got them.

Your semiannual rate is wrong.

[ImBruces]

EAR = (1+0,081483747/365)³⁶⁵ than -1 and multiply by 100, got 8,48 for daily lol

well I applyed that formula…

[S2000magician]

The rate of 8.1483747% is the EAR.

[ImBruces]

How can I get the other values than?

[S2000magician]

What’s the formula that relates EAR to the continuously compounded rate?

What’s the formula that relates EAR to stated rate?

[ImBruces]

EAR = ers − 1 ?

[S2000magician]

What’s ers?

[breadmaker]

It makes me very happy to see you doing this kind of problem by hand in order to understand the mechanics.

I know you use the HP, but the BA II has a nominal to EAR converter. Does the HP have something similar? It would save you time and grief.

[ImBruces]

@breadmaker

It makes me very happy to see you doing this kind of problem by hand in order to understand the mechanics.

I know you use the HP, but the BA II has a nominal to EAR converter. Does the HP have something similar? It would save you time and grief.

I don`t think the HP12c has a function like that…

You mean the BA II you don`t need to know the EAR formula to convert?

The calculator does it all?

[ImBruces]

@S2000magician

What’s ers?

I dont know its the formula that is in the book for EAR…

[S2000magician]

@ImBruces

@S2000magician

What’s ers?

I dont know its the formula that is in the book for EAR…

No, it’s not.

Maybe you’re forgetting a superscript?

[ImBruces]

The only way I found to do is 500000 CHS PV 800000 FV 12N 0 PMT

asks for i = 3,9944 than i multiply for 2 get nearly 8% semianually compounded

Pretty sure there`s a alternative to do it through, was looking for it…

[S2000magician]

@ImBruces

The only way I found to do is 500000 CHS PV 800000 FV 12N 0 PMT

asks for i = 3,9944 than i multiply for 2 get nearly 8% semianually compounded

Pretty sure there`s a alternative to do it through, was looking for it…

That’s the semiannually compounded stated rate:

Stated rate_semiannual = [(1 + EAR)^1/2 – 1] × 2

More generally, for compounding n times per year:

Stated rate__n_ = [(1 + EAR)^1/n – 1] × n

Now . . . what about the continuously compounded formula?

[S2000magician]

@ImBruces

The only way I found to do is 500000 CHS PV 800000 FV 12N 0 PMT

asks for i = 3,9944 than i multiply for 2 get nearly 8% semianually compounded

By the way: there’s your answer: C.

[ImBruces]

@S2000magician

@ImBruces

The only way I found to do is 500000 CHS PV 800000 FV 12N 0 PMT

asks for i = 3,9944 than i multiply for 2 get nearly 8% semianually compounded

Pretty sure there`s a alternative to do it through, was looking for it…

That’s the semiannually compounded stated rate:

Stated rate_semiannual = [(1 + EAR)^1/2 – 1] × 2

More generally, for compounding n times per year:

Stated rate__n_ = [(1 + EAR)^1/n – 1] × n

Now . . . what about the continuously compounded formula?

In what page of the CFA curriculum is this formula?