Time Value Tables

The following are three tables that are intended to help you appreciate the effects of Time Value of Money:

      1.   The future value of a single payment
2.      The future value of a series of payments (annuity payments)
3.      An expected monthly payment table

Try to visualize how time and rate affects the value of money.

(1) The Future Value of a Single Payment of $10,000

It answers the question: How much can you expect to make
from a single investment?
(Payment made in the beginning of the year)

Years / Rates	5	10	20	25	50
4%	12,167	14,802	21,911	26,658	71,067
6%	13,382	17,908	32,071	42,919	184,202
8%	14,693	21,589	46,610	68,485	469,016
10%	16,105	25,937	67,275	108,347	1,173,909
12%	17,623	31,058	96,463	170,001	2,890,022
15%	20,114	40,456	163,665	329,190	10,836,574

Notice how time builds wealth even at the lower return rates. This is the advantage that young investors have.

This is also one reason why some seniors are able to pass along substantial inheritances to their children. For many retirees, their spending drops, and if their income covers insurance, living and overhead expenses; their nest egg is allowed to grow untouched; and it adds up.

Below is a future value table for annuity payments. Annuity payments are amounts paid or received for a specified number of periods. The table below is valuable when determining future IRA and 401k account balances. These tables, however, while useful, are fixed. They don’t reflect an increase or decrease in the periodic amount saved. Normally, once you start working your pay increases over the years through a combination of merit raises, promotions and new positions by changing employers. For self employed individuals compensation rises over time as your business grows and prospers. At some future point, however, it’s not uncommon for your earnings to decrease and a young adult starting a career may make as much as the senior leaving the position. Expect your IRA contributions to fluctuate as you travel your journey through life.

(2) Future Value of Annual Installment Payments of $2,000

It answers the question: How big will your IRA nest egg be?
(Payments made in the end of each year)

Year/ Rate	5	10	20	25	50
4%	10,833	24,012	59,556	83,292	305,334
6%	11,274	26,362	73,571	109,729	580,672
8%	11,733	28,973	91,524	146,212	1,147,540
10%	12,210	31,875	114,550	196,694	2,327,817
12%	12,706	35,097	144,105	266,668	4,800,037
15%	13,485	40,607	204,887	425,586	14,435,433

Charts, graphs and tables can look good on paper and in theory. They rarely, however, factor in life situations. The time you take off to raise your children. The long spell of choppy employment in your forties or fifties. The unwise and expensive IRA withdrawals to pay college or medical bills. A trip with your aging parents to Europe. Not to mention at least one Enron type investment. Nevertheless, a consistent savings approach, along with reinvesting interest and dividends earned from your investments, usually builds wealth over time.

Accumulating money is not the whole game. Time Value of Money is also used to compare alternative strategies and assumptions as you proceed through your working years and retirement. For example: 1) how much of your nest egg do you live off, versus how much to you leave to your heirs as inheritance; 2) how much money can you withdraw from your savings and still have money at some future date. You need to make some basic assumptions, such as: When will you be retiring, and how long are you going to live? What market rates can you expect? The payment schedule below should give you some idea about the payments you can expect from your savings.

(3) Monthly Payments from $200,000 of Savings

It answers the question: how much monthly income will your nest egg provide?

(No remaining balance at the end)

Years/ Rates	5	10	20	25	30	35
4%	3,671	2,018	1,208	1,052	952	883
6%	3,847	2,209	1,426	1,282	1,193	1,135
8%	4,028	2,410	1,662	1,533	1,458	1,411
10%	4,214	2,621	1,914	1,802	1,741	1,705
12%	4,405	2,841	2,180	2,086	2,037	2,011
15%	4,699	3,187	2,601	2,530	2,498	2,483

$200,000 doesn’t look like much when you factor in inflation, and realize that it must last your entire remaining life. That is why annuities with life-time payments are purchased.

While the Time Value of Money concepts are relatively easy to understand, the underlying mathematics is difficult. The best way to learn about the time value of money is to experiment with a calculator; it’s fun and easy.

Just know the basics! The guys who “slice and dice” cash flows for mortgage backed securities, get wild with this stuff. However, it all boils down to understanding a few keys and keystrokes on the calculator.

Mathematically, it is about solving an equation involving four basic factors: Amount, Payment, Rate, and Time.

Next review how to use the time value functions on: The HP 12C calculator.