I am afraid I hit a brick wall with this question. It goes as follows- Jack opened up a savings account 18 years ago with the intention of achieving $ 150000. He made equal monthly 400 dollars deposits for 12 years, and the accumulated balance was left to compound for the other 6 years at 7% per annum. I want to work out the EAR for the first 12 years. I know I should assume monthly compounding, but am generally stuck. Should I work out the present value of the 6 year deposits first?

Any help would be greatly appreciated. Cheers

This is a model as to how you work out the
monthly effective rate.

Effective Rate:-

Monthly compounding at 7%.

1 1.000000 1.005833
2 1.005833 1.011700
3 1.011700 1.017601
4 1.017601 1.023537
5 1.023537 1.029507
6 1.029507 1.035512
7 1.035512 1.041552
8 1.041552 1.047628
9 1.047628 1.053739
10 1.053739 1.059885
11 1.059885 1.066067
12 1.066067 1.072286

ANSWER = 7.2286%

Are you sure that it's compounded yearly or monthly or quartly is not mentioned?

oh sorry I did'nt see that that you want it monthly
I think that you should work out this
EAR=(1+quoted rate\m)*m-1
=(1+.07/12)*12-1
= .7229

It stated clearly it was monthly.
The rate is 7.2286% depending on the
Number of decimals for accuracy.

.7229 does not make sense.
TRY .07229.

Yes what you have said is right it's .07229
I'm so sorry I was so hasty

Thank you for your quick response! Although to tell you honestly, I am a bit confused as to the answer. I think the thing with this question is that the 7% is annual compounding, and that is for 6 years. The other 12 years are unknown % at monthly compunding. Is there a way to work it out without tables, and using formulas?

I don't know if I'm completely right but I'll try to help
first as you said you must get the present value of the 6 years deposit
p=150000\(1.07^6)= 99951.33

then you apply the same rule to bring the value of I before 12 years
99951.33=400(1+i)^144
99951.33\400=(1+i)^144
then (1+i)= 1.0390
I=.0390

Are you there?

Yes, thank you. I thought that it is the process as well, but for some reason it looks too easy.I might have build up the complexity of it in my head though. Thank you for your answer

You're welcome:)