# Solving for Number of Periods

I’m having issues while computing for N given the PV, PMT and I/Y The question is : Imagine that you have just retired, and that you have a nest egg of \$1,000,000. This is the amount that you will be drawing down for the rest of your life. If you expect to earn 6% per year on average and withdraw \$70,000 per year, how long will it take to burn through your nest egg (in other words, for how long can you afford to live)? After entering the data as follows: 6 into I/Y, -1,000,000 into PV and 70,000 into PMT, On pressing CPT N instead of 33.40 withdrawals the answer I get for N is 35.13 I’m constantly facing this problem while solving for N. Any idea as to how I could get the answer as 33.40? Any help would be appreciated. EDIT: So after a lot of trials I reset my calculator and now the answer is finally matching. Sorry for the trouble but does anyone have an idea as to what could be triggering my earlier problem so I can avoid it during the exam? I don’t want to lose all settings during the exam.

If you have an ordinary annuity the way you’ve done is correct.

Hovewer, if you retire the \$70,000 starting right from retiring date and at the beginning of every following year (annuity due) you either have to set your calculator to BGN mode or use for PV-(1000,000/1.06) = -943,396 and solve for N. This will give you 28.37 yrs. until depletion of your savings.

Best,

Oscar

I did the same on my calculator and i got 33.4 years…

put 0 in FV

For N=35.13, you set P/Y=1 and C/Y=4 (1 payment per year, 4 interest compounding periods); for N=33.4, you set P/Y=C/Y=1 (1 payment per year, 1 interest compounding period per year).

When you are doing a TVM problem, you need to check your P/Y and C/Y settings too!!

And check for BGN/END too!!!

One thing I was asking mayself: It is possible to calculate the priods using internannual compounding without changing C/Y.

I tried to calculate the periods by quarterly compounding by entering I/Y=6/4 and PMT=70,000/4, PV =-1,000.000 and solving to N and dividing the result by 4 but instead of getting 35.13 I get 32.67.

Any Idea?

Thank you! Tried again and that indeed was the problem. Also thanks to everyone else who tried to help

I would set P/Y and C/Y as appropriate (C/Y=P/Y=1 for the original example). Using I/Y=6/4 means you are assuming 6% nominal compounded quarterly, whereas the original problem assumed 6% effective annual. Furthermore, changing the timing of the cash flows from \$70,000 once at the end of the year to \$17,500 at the end of every 3 months will throw off the calculation.

I understand that the original example used annual compunding.

I am just wondering if there is a solution if it were quarterly compounding without changing (C/Y / P/Y)?

I get 34 exactly. What am I doing wrong?

I tried calculating how long it would take to double 10M to 20M @ 7% annual compounding and I get:

PV -10,000,000

FV 20,000,000

i 7

when I press n, I get 11 exactly. Example 19 reading 5 gets an answer of 10.24 for this. But they used logs which you don’t have on a financial calculator so not much use.

10 000 000 * (1.07) ^n = 20 000 000

1.07^n =2 000 000 / 1 000 000

n ln (1.07) = ln 2 (there’s a ln button on your calculator for natural logarithm)

n = ln (2)/ln (1.07)

n = 10.2447683

On your BA II, P/Y=C/Y=1, I=7, PV=10 000 000 FV = -20 000 000 PMT =0. Now my BAII bit the dust some time ago, but you should get N=10.24 when you hit CPT.

You might also want to check how many digits your calculator is displaying.

In general. trying to find the correct setting for P/Y on your calculator has very little upside and large potential for screwing you up.

Instead, train yourself to always think in term of periods. And remember that a period need not be a year. Second, be consistent - use the interest rate that matches the period. And if you’re wondering, the interest rate would be the % change in a dollar over whatever you’ve defined as a period.

30-year, 6% monthly mortgage? A period is a month, N=360, and I/Y = 6/12.

Ten years of annual investments into an account that pays 10% annually, compounded semiannually? N=10 and I = 10.25% (in an account that pays 10% semiannually, a dollar grows to \$1.1025 in a year’s time).

Future Value in 8 years of a single lump-sum investment in that same 10% apr account with semiannual compounding? Either treat 6 months as a period and use N=16 and I/Y = 5 or make a period a year and use N=8 and I/Y = 10.25%.

The number of digits is set to 9, so that’s not the problem.

Ah there is too a natural logarithm button. I didn’t try hard enough looking for it before. Can get the answer with the calc now.

But still curious if the TV buttons can be used to calculate this also.

What is P and C in your expalnations? Y is obviously the number of compounding periods per annum, although I’m not sure what Y actually stands for, it’s certainly not yield. But yer, what is P and C?

I have more or less got the period thinking under my belt, that’s not the problem, I’m just unable to get the answer using TVM buttons.

EDIT: Found this:

“The HP 12C always gives an integer answer when solving for N.”

So looks like logs is the only route to take for these calculations.

P/Y: number of payments per year, C/Y: compounding frequency per year

Keeping P/Y and C/Y at 1 will work, but you have to ensure your value of I is set correctly! I’m in the “setting P/Y and C/Y as appropriate” school, so I won’t bother rehashing my counterarguments.

If the payment was quarterly instead of yearly, you simply divide the quoted yearly rate by 4 (they would always give a nominal yearly rate that’s compounded quarterly, if its a quarterly question). Your answer in N would then be in quarters, divided by 4 to get to the years.