Suppose that you are offered an investment that will cost $925 and will pay you interest of $80 per year for the next 20 years. Let's look at an example of solving for the interest rate: Any time you are solving for N, I/YR, or PMT there is the potential for a wrong answer or error message if you don't get the signs right. As has been mentioned numerous times in this tutorial, be sure to pay attention to the signs of the numbers that you enter into the TVM keys. Solving for I/Y works just like solving for any of the other variables. Example 2.4 - Solving for the Interest Rate Assuming that you can live for about a year on the last withdrawal, then you can afford to live for about another 34.40 years. Now, press N and you will see that you can make 33.40 withdrawals. 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)? Assume that your first withdrawal will occur one year from today (End Mode).Įnter the data as follows: 6 into I/YR, -1,000,000 into PV (negative because you are investing this amount), and 70,000 into PMT. This is the amount that you will be drawing down for the rest of your life. Imagine that you have just retired, and that you have a nest egg of $1,000,000. Solving for N answers the question, "How long will it take." Let's look at an example: Example 2.3 - Solving for the Number of Periods Now, press PMT and you will find that you need to invest $2,670.21 per year for the next 18 years to meet your goal of having $100,000. Let's enter the data: Type 18 into N, 8 into I/YR, and 100,000 into FV. In other words, it is a regular annuity.) (Note that, for now, we are assuming that the first investment will be made one year from now. In this case, saving for college will be easier because we are going to spread the investment over 18 years, rather than all at once. Recall that we previously determined that if you were to make a lump sum investment today, you would have to invest $25,024.90. If you believe that you can earn an average annual rate of return of 8% per year, how much money would you need to invest at the end of each year to achieve your goal? Furthermore, assume that you have determined that you will need $100,000 at that time in order to pay for tuition, room and board, party supplies, etc. Suppose that you are planning to send your daughter to college in 18 years. Let's look at that problem again, but this time we'll treat it as an annuity problem instead of a lump sum: On the previous page, we looked at an example about saving for college. Or, maybe you want to know how much you will need to save each year in order to reach a particular goal (saving for college or retirement perhaps). For example, you might want to know how much a mortgage or auto loan payment will be. We often need to solve for annuity payments. How much would you have to repay?Īll we need to do is to put a 0 into PV to clear it out, and then press FV to find that the answer is -15,192.92972 ( a cash outflow).Įxample 2.2 - Solving for the Payment Amount Now, suppose that you will be borrowing $1000 each year for 10 years at a rate of 9%, and then paying back the loan immediate after receiving the last payment. Again, this is negative because it represents the amount you would have to pay (cash outflow) to purchase this annuity. Now press PV to solve for the present value. Enter the numbers into the appropriate keys: 10 into N, 9 into I/YR, and 1000 (cash inflow) into PMT. Press Shift C to clear the financial keys. In this case we need to solve for the present value of this annuity since that is the amount that you would be willing to pay today. If you can earn a rate of 9% per year on similar investments, how much should you be willing to pay for this annuity? Suppose that you are offered an investment which will pay you $1,000 per year for 10 years. In a regular annuity, the first cash flow occurs at the end of the first period.Īn annuity due is similar to a regular annuity, except that the first cash flow occurs immediately (at period 0). In this section we will take a look at how to use the HP 10BII to calculate the present and future values of regular annuities and annuities due.Ī regular annuity is a series of equal cash flows occurring at equally spaced time periods. In the previous section we looked at the basic time value of money keys and how to use them to calculate present and future value of lump sums. Are you a student? Did you know that Amazon is offering 6 months of Amazon Prime - free two-day shipping, free movies, and other benefits - to students? Click here to learn more
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