To set the number of periods per year on the TI BA II +:
B. if calculator shows PMT= 948.27
12 x 21 [=] [N]
[CPT] [PV] = $117,380.78
It is easy to make a mistake with a financial calculator, so the best way to reduce the mistakes is to have a rough idea of what the answer should be.
1. Assume that Steve has $15,000 in his IRA which earns 6.8% annually. Steve also makes the maximum annual contribution of $2,000 to this account which he puts in at the END of the year. Ignoring taxes how much money should Steve have at the end of 25 years
You can get a rough idea of the correct answer - Look at the Future Value of an Annuity table or my Time Value of Money tables on the 360 web page.
7%, 25 years, $1 -> 5.4274, so 15000 -> 5.4274 x 15000
= 81,411
7%, 25 years, $1/year -> 63.2490. So 2000/year -> 63.25 x 2000
= 126,498
So total is $207,909
TI BA II Plus keystrokes
[2nd][P/Y]1 [Enter]
[2nd][QUIT]
{to set for ANNUAL payments and compounding periods}
If you see BGN above the number display, then
[2nd][BGN][2nd][SET]
{you should NOT see BGN now above number display }
[2nd][QUIT]
15000 [+/-] [PV]
6.8 [I/Y]
2000 [+/-][PMT]
25 [N]
[CPT][FV]
{display will have FV = 200,615.517, which is reasonably close to the results
using the tables - remember, table results are based on 7% rather than 6.8%}
2. Assume that you contribute $100 at the beginning of each
month to a small stock 401(k) fund that is expected to have a 15.5% annual
nominal rate of return.
A. What should your accumulation be (in nominal terms) at the end of 51 years?
How would you know whether the answer is correct or not?
Look at a Future Value of an Annuity table, or my Time Value of Money tables on the 360 web page.
The future value of $1 per year for 50 years at a 16% rate of return = $10,435.650
In the problem, you would contribute $1200 per year for 51 years. (To get credit, you would have to use monthly calculations, but we are just trying to get a rough idea)
If $1 per year for 50 years grows to $10,435.65
Then
$1200 per year for 50 years would grow to
1200 x $10,436
= $12,522,780
If you properly enter the numbers in your financial calculator, you would obtain, contributing $100 at the beginning of each month for 51 years, with a 15.5% annual rate of return, $20,200,847
It is higher than the result you obtained from the table, although the effect of investing at the beginning of each month (instead of the end of each year, as assumed in the table) and having an extra year results in the much higher amount.
The advantage of checking the table, though, is that you would at least realize that the result is possible.
Key strokes for TI BA II Plus financial
calculator
[2nd][P/Y]12 [Enter]
[2nd][QUIT]
{to set for monthly payments and compounding
periods}
If you do not see BGN above the number display,
then
[2nd][BGN][2nd][SET]
{you should see BGN, if not repeat [2nd][SET]
}
[2nd][QUIT]
51 [2nd][N] [N] [ENTER]
{N=612 will be displayed}{note that you should
have hit the N key twice}
The alternative method is to multiply
the number of years by 12, so
51*12 [N]
15.5 [I/Y]
100 [+/-][PMT][ENTER]
0[PV]
[CPT][FV]
{display will have FV=20,200,847.49
~~~~~~~~
3. Finding a length of time.
The basic idea with financial calculators
is that you should know any 4 of the 5 basic values
N, I/Y, PV, PMT, and FV
you enter numbers for any 4 of them, then
hit the CPT key to compute the fifth value
If you have hit [2nd][QUIT] all
of these start out at 0, so, for instance, in the above example, we did not
bother entering
0[PV][ENTER]
B. What if you wanted to know how long
it would take for your $100 per month to reach $100,000?
If you had not done so before
[2nd][P/Y]12 [Enter]
[2nd][QUIT]
{to set for monthly payments and compounding
periods}
If you do not see BGN above the number display,
then
[2nd][BGN][2nd][SET]
{you should see BGN, if not repeat [2nd][SET]
}
[2nd][QUIT]
15.5 [I/Y]
100 [+/-][PMT]
100000 [FV]
[CPT] N
N=204.24
In other words, just over 204 months, or
17 years
Of course, this would not account for inflation,
so a new Mercedes might cost $100,000 then.
~~~~~~~~~
What if you wanted to find the mortgage
balance?
You could study your calculator handbook
for use of the Amort key, but the basic methodbelow is fine also.
(They might come out with slightly different
results)
2. Assume you bought a $300,000 home,
making a $100,000 downpayment.
The mortgage is $200,000, with a 6% annual
interest rate. You decide to finance it for 30 years.
A. Find the monthly payment,
Key strokes for TI BA II Plus financial calculator
[2nd][P/Y]12 [Enter]
[2nd][QUIT]
{to set for monthly payments and compounding
periods}
If you see BGN above the number display,
then
[2nd][BGN][2nd][SET]
{you should NOT see BGN }
[2nd][QUIT]
30 [2nd][N] [N][ENTER]
{you should see N=360}
alternative method
30 [x] 12 [N]
6[I/Y]
200000 [+/-][PV]
0 [FV]
[CPT] [PMT]
will show PMT = 1,199.10
B. Find the mortgage balance after 10
years.
360-120=240
240 [N][ENTER]
the PMT, FV, and I/Y registers should still
have the numbers from the previous calculation, but if not, you would need
either repeat the steps above or do the next 3 steps
0[FV]
1191.10 [PMT]
6 [I/Y]
[CPT][PV]
{you should see PV = -167,371.45}
Note that you would have made payments
of $143,892
(1199.10 x 12 months/year x 10 years)
but your balance only decreased by about
$32,628.55
Your balance after 10 years is 83.686%
of the original balance.
Now, how can you tell if you have the right
answer/
If you consider mortgage balance tables
such as on the 360 web site,
the mortgage balance should be LOWER than
the original amount borrowed, but in the first 10 years of a 30 year mortgage,
the balance will decrease very slowly.
Below is an example of a mortgage balance
table for a $100,000 loan,
6% annual interest rate, 30 year term
So, for instance, if we ask you to find the mortgage balance of a 30 year loan after 10 years of payments, the result will probably not be too far from 84% of the original balance.
Year remaining
balance
1 98772
2 97468
3 96084
4 94615
5 93054
6 91398
7 89639
8 87772
9 85790
10 83686
11 81451
12 79079
13 76561
14 73887
15 71049
16 68035
17 64836
18 61439
19 57832
20 54004
21 49939
22 45623
23 41041
24 36177
25 31012
26 25529
27 19708
28 13528
29 6966
30 0