Variable Force of Interest Trap

[mjlee08]

In ASM (6th edition, pg 58), Cherry makes note that we shouldn't fall into the variable force of interest trap, but I'm afraid I already have.

My understanding is that you have to be careful if the investment is not made at time 0 when investing with a variable force of interest.

This is just the first part of the question:

Joe deposits 10 today and another 30 in 5 years into a fund paying simple interest of 11% per year. Find the accumulated value after 10 yrs.

At the beginning of the manual, I would have said
10(1+(10)(.11)) + 30(1+(5)(.11))

But after reading about how things change when you invest at some time other than 0, (and since the force if interest varies for simple interest) I thought the accumulated value would be:

10(1+(10)(.11)) + 30(1+(10)(.11))/(1+(5)(.11))

What is wrong with my thinking?:skeptical:

[Elk]

OK, I could use some help on this too, but I'll try and shed a bit of light.

Well, with the force of interest as in Harold Cherry's paragraph, the force of interest is specifically measured from a certain date. In my edition (the 5th), the investiment is made at time 2, so you divide by a(2).

I think it's different for simple interest. The force of interest for simple interest diminishes over time because you get less and less for the amount you originally invested. You have more in your account as time goes by but the interest is always the same. Not really fair.

In your example, the new investment at time 5 would have the same force as the original investment did at time 0. (I think that's right)


So, from time 5 to time 10, you actually have 2 separate forces of interest working. So, you have to treat the two as separate investments as you did the first time.

Make any sense? Can anyone add or correct anything here?

[JDav]

Without going into a tremendous amount of detail, let me give it a quick try:

You're right, that simple interest is not a constant force of interest. But your formula that you're trying to use (the second one, where you're dividing) is still using a constant force. The technique will work like you think, but you actually have to model the simple interest correctly.