# simple TVM question

Can you guys help me and do this strictly in END mode? I can’t seem to get the correct answer. In the first line I get PV as \$45059.70. Then I have an annuity of 9 years instead of 10, but I get PMT as \$3049.59.

If, however, I discount it by 10 years, I get \$2,567.69. Multiply this by the discount rate of 12% and I get the correct answer of \$2,875.81.

Why is there a discrepancy? And also on the exam, is it better to leave your calculator in END mode and be consistent or should I change from END to BGN depending on the question?

The only difference between END mode (ordinary annuity) and BGN mode (annuity due) is that for present value the former is discounted one extra period, and for future value the latter earns interest for one extra period.

Thus, any problem that _ should _ be done in BGN mode _ can _ be done in END mode; just multiply the final answer by (1 + i). I wouldn’t do it that way, but there’s no reason you can’t; it’ll give you the correct answer.

I’d suggest leaving you calculator in END mode in general, only switching to BGN mode when you need it for a specific calculation, then switching it back when you’re done.

In the final analysis, you should do whatever works for you: the method that you won’t forget when under the pressure of the test.

Best of luck.

I know that the difference is one period. Out of all the CFA topics, TVM is the one I know I can ace for sure. That is why I’m confused as to why I can’t get the answer in my example above.

I’m not going to worry about this too much though. I was hoping to stay in END mode for the exam but if I have to, I’ll just switch back and forth.

EDIT: But if someone could tell me what is wrong with the above, that would be great.

There’s nothing wrong with the above:

You got the correct answer: you did it in end mode for the correct number of periods, then multiplied by (1 + 12%).

Switching between BGN and END modes is far simpler than trying to make extra adjustments to calculated figures.

Here is yet another way to do line 1 in END mode: of course, pick END mode. Set N=4 leaving all other values the same. This will produce a PV of 37,966.87. Add 12,500. This takes advantage of the fact that an n-year annuity due is identical to an immediate annuity for (n-1) years plus 1. It works, but all it does it create extra keystrokes for you.

This explanation has been helpful but can someone explain further why the switch between end and begin mode. What does end and begin mode represent

END mode means that the periodic payments are made at the end of each period; BGN mode means that the periodic payments are made at the beginning of each period.

If you set today to time 0, then the payments in END mode would be made at times 1, 2, 3, . . ., while payments in BGN mode would be made at times, 0, 1, 2, . . . . Thus, to discount back to today the first payment, in END mode you discount it for one period; in BGN mode you dicsount it for zero periods. The second payment in END mode would be discounted for two periods; in BGN mode, one period. And so on.