Hi,
Can anyone help to solve this question with Calculator?
A saver deposits the following amounts in an account paying a stated annual
rate of 4%, compounded semiannually:
Year End of Year Deposits ($)
1 4,000
2 8,000
3 7,000
4 10,000
At the end of Year 4, the value of the account is closest to:
A $30,432
B $30,447
C $31,677
Correct answer is : $30,447.
But when I enter CF0:0, CF1:4,000, CF2:8,000, CF3:7,000 and CF4:10,000 I/Y= 2 then hit NFV and I get $29,708.
What am I doing wrong?
I’m using a BA 2 Plus Pro, so the process might be a little different if you are using an HP:
first, make sure you clear the memory, just to make sure it doesn’t mess with calculations.
press CF to enter the cashflow sheets in the calculator
press the down arrow and insert the values
C01 = 4,000, let F01 = 1
C02 = 8,000, let F02 = 1
C03 = 7,000, let F03 = 1
C04 = 10,000, let F04 = 1
then, press 2ND QUIT to exit the cashflow sheet
press 2ND ICONV to convert the given nominal interest rate into the effective interest rate.
NOM = 4, press enter and then down twice,
C/Y = 2, press enter and then down twice.
EFF, press CPT. The calculator will give you 4.04 as the answer.
Press 2ND QUIT.
now, go back to the cashflow sheet.
press CF and then NPV
I = 4.04, press enter, then press twice.
NFV, press CPT.
The calculator gives 30,446.90696 as the answer.
Thanks so much for an explanation. But why do we have to calculate in “effective rate”? How would we know that we have to use an effective rate?
The I in the calculator assumes the effective interest rate.
In other questions, we never converted stated rate to effective rate to calculate PV or FV. I’m still not understanding why in this question?
The calculator assumes the effective interest rate when calculating the FV through the cashflow sheet function. If you want, you could calculate the same quantity using the interest rate of 2% per half-a year (1 + .04/2 = 1.02). If you solve this way, you need to remember that the time period is in 6 months, not years.
4,000 * 1.02^6 + 8,000 * 1.02^4 + 7,000 * 1.02^2 + 10,000 = 30,446.90696
this is equivalent to using the annual effective rate of 4.04% per year (where the period is 1 year, not 6 months).
Thanks, millions for explaining.
You’re very welcome. 
If you want to use I=2, you will have to insert 0’s between the payments:
C01=0 F01 =1 C02=4000 F02=1 c03=0 F03=1 C04=8000 F02=1, etc.
Better just to use 4.04% as the EAR to match the payment frequency! 
sounds great, thanks so much!
Effective rate is 4.04 . (1+ 4%/2)^2 not 4/2 otherwise your steps are correct
Would you like to share other question so that we can compare. There is always something in the question that we tend to overlook or the wording is a bit odd