Ask Me Help Desk - Help with Finance Questions

Quote:

1. Mitchell borrows $50,000 from his father and promises to pay it back over the next 10 years, making equal annual end of the year payments. Calculate the amount of each payment if the annual interest rate is 9%.
I know this is an ordinary annuity. But do I divide the $50,000 by 10 and then multiply that number by the 9% annuity rate off the PV chart?

No. You have to keep in mind that each payment is going to include some interest. Just for instance, Mitchell originally borrows $50,000, which exists for an entire year before he makes a payment. At 9% that payment is going to include $4500 of interest. We don't know the payment amount, but it will have $4500 of interest and the rest of it will go towards the $50,000 as principal. This then reduces the amount for the second year (to something we don't know). So the interest on the second year will then be lower, but the total payment will remain the same, so more will be left to go towards principal. Etc.

As you can see, even though the payments are equal, they include part interest and part principal, both of which change, but the total remains equal. By time he gets done paying it, he'll have paid more than $50,000 cause it will include interest. It's nowhere near as simple as just dividing $50,000 by 10 years. Solving it is no more difficult, but I mean the concept behind it is much more complicated. While it seems like a big mess, those charts have all this built into them. You have to decide which chart, but then you just pull off a number, multiply or divide, and poof you have a final answer.
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I'm not going to comment on the rest. Instead I'm going to throw some things at you at to try to help figure out what is what, then let you see if you can just apply it. Also don't forget everything from #1 above because it'll be relevant for any annuity.

Personally, I think it's a good idea to decide first whether you have a lump sum or an annuity, because that will change how you have to think about the rest of the problem.

A lump sum starts as a present value, has interest ONLY added onto it over some time, and therefore grows in size, until it becomes a future value. There are no payments added to or taken away from it. Only interest gets added. It does not matter what direction the money goes -- i.e. whether you stick it into a savings account and allow it to grow, or borrow it and have to pay it back, cause it's still going to grow into a bigger payment that includes interest. Mathematically they all work the same.

With a lump sum, you have both a present value and a future value - present grows into future. The one you are solving for is the chart you want to use. This means if you have the present value, you're solving for the future value, and therefore use the future value chart. Or vice versa.

An annuity involves some type of payments, deposits, etc. In order to qualify as an "annuity" for our purposes, the payments must be equal and at equal time intervals.

In an annuity situation, normally the present value is literally today's value and a future value is some time in the future. However, there are exceptions. What you really need to look at is where the payments are relative to the total.

For instance, in a present value situation, you will start with some total amount. You will then remove equal amounts from this. It will earn interest in the meantime. When you remove a payment, whatever's left still earns interest but less. Etc. These payments will continue to come off until it goes to zero. There is no future value. Examples of this are taking money from your retirement account, or paying off a loan. Make note of the fact that we start with some amount and remove the payments, taking it eventually to zero. You can calculate something that doesn't happen until the future, say your retirement 30 years from now, but if you're taking payment off it, it's still a present value cause it's relative to the payments.

In a future value situation, we start with nothing. We then put payments into something and let them start collecting earnings. Then we continue to add payments over time, until it grows into some future amount. We started with nothing and there is no present value. Note it's a future value cause it's future relative to the payments. Examples are saving for something needed in the future (retirement, a machine for a company), or just anything else that will grow over time, like sales growing 10% every year, etc.

Notice with annuities that present value and future value never exist together. (They may exist in the same problem, but would not be used at the same time.) They exist relative to a payment, which I keep underlining for a reason. ;) So when trying to figure out whether it's present or future, think about where it is relative to the payments. And that is also the chart you use.

That's the essence. Because of some of what I saw here, I'm going to add some stuff. When dealing with annuities, you can also have to solve for the payment itself. Some books can have a special chart for this. However, I've only ever seen them in business math classes, not accounting and finance books. So we may have some division involved.

Best way to think of this:
Payment x Factor off Chart = Present or Future Value
Normally you'll have the payment, and you can look up the factor on the chart, and you just multiply to get your present or future value. What if instead you have your present or future value and have to solve for the payment? You still get the number off the chart, but now you have the "answer" and the factor, and have to divide to go backwards and get back to the payment.

Also, when you have a series of unequal payments, this is not an annuity. This has to be treated as individual lump sums, using the lump sum charts, and then add up all the answers. Use 1 period for the 1st one, 2 periods for the 2nd, etc.

As a general rule, whenever you want to compare things, you will be doing present values. If you had the choice to get $20,000,000 now or $1,000,000 payments for the next 20 years on a lotto, you're comparing that series of payments to something you will get TODAY. So the $20 million is already its own present value. In order to make a comparison of future cash flows, you have to bring them back to a present value. There are times you may compare future values, but it's not typical.

OK, have at it and see what you can do. (And take the $20 million today.)