Can anyone have a look at what I did wrong with the calculator?
Q: An investment of $20,000 for 4 years that pays 3.5% per year. The interest payment of $700 (20000*3.5%) are reinvested at an annual rate of 2% compounded monthly. Find the FV of the interest payments.
A: I know the correct answer is 2885.92
1st interest payment at T=1 to T = 4 gives 700*(1+0.02/12)^3x12 = 743.25
2nd payment at T =2 to T = 4 gives 700*(1+0.02/12)^2x12 = 728.54
3rd payment at T =3 to T = 4 gives 700*(1+0.02/12)^12 = 714.13
4th payment at T =4 simply = 700
Total = 743.25 + 728.54 + 714.13 + 700 = 2885.92
But when I input this into the calculator using the functions it gives a different answer: N = 48 (4 years x 12 compounding period), i/y = 2/12, PMT = -700, cpt fv = 34,950
If I ignore the compounding effect, it gives the right answer N=4, i/y = 2, PMT = -700, cpt fv 2885.
Because 700 is an annual amount but the periods are monthly. So you’re basically inputting 12 $700 payments per year. Interesting question, I don’t know how to solve it on the calculator. Writing out each year like you did is quite a bit of work for an exam setting.
Thanks for your reply. This is one of the official questions in cfai actually. So the N= no. of compounding period and i/y = rate/no.of compounding period are only applicable for PV->FV or FV->PV but not when the PMT time interval is different… It seems that we should ignore the compounding effect here in the calculator. Any more thoughts from anyone?
You are correct, but incomplete. Since PAYMENTS take place annually, you must use an ANNUAL rate. In this case, it’s the EAR of 2% APR, compounded monthly.
In general, it’s best to leave P/Y set to 1, and think in terms of PERIODS, not years. Then make sure you’re using the interest rate PER PERIOD and the number of PERIODS. In this case, the payments take place ANNUALLY, so the interest must also be on that basis. And the interest rate will be the % change in a dollar over teh period in question. In this case, that’s 2.02%
So, for exam purposes: when they say to us X annually rate coumpounded M; and if our payments are annually, we have to put in the calculator the X annual rate or make this X annual rate on a EAR basis. That is, with our example, not putting 2% but 2.02% (1+(2/12)^12-1. Right?
(1 + 0.02/12)^12 - 1 (decimals and parentheses are important)
For lump sum problems you can adjust either the interest rate or the number of periods. In other words, a FV of a lump sum problem for 3 years at 10% APR compounded semiannually can be solved either as N=3 and I=10.25% or as N=6 and I=5%.
But for annuity problems, you can’t adjust the frequency of the payments (they are what they are). So, you must adjust the interest rate to the periodicity of the cash flows. The rule is that you use as the interest rate the percentage change in the value of a dollar over the time frame between annuity payments. That’s all an effective rate is. And while you typically see them as effective ANNUAL rates, it’s not limited to that. As an example, there’s no reason you couldn’t have a BiAnnual annuity (i.e. payments every two years), If you did and the ANNUIAL rate was 10%, you’d use 21% ((1.1)^2 - 1) as your interest rate.