# Tutoring financial math, spreadsheets might be used. The tutor shows how to find the monthly payment on a loan using Excel.

In yesterday’s post I tell how to find the amount against the principal that a certain payment removes, using the ppmt function.

Perhaps more directly, a person might wonder how to calculate the monthly payment in the first place. Here’s how:

Example: Imagine a 25-year, \$100,000 loan at 4% compounded monthly, with monthly payments as well. Find the monthly payment.

Solution: Using Excel, you’d enter

=pmt(4%/12, 300, 100000)

300 means the total number of payments: 12 per year for 25 years. The payment is assumed to be at month’s end.

Hopefully, the answer will come to -527.84, the negative meaning money paid out (as opposed to received).

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring financial math, amortization arises. The tutor mentions the Excel function for it.

Example: For a 25-year loan of \$100,000 at 4%, compounded monthly with monthly payments, what is the amount against the principal of the 101st payment?

Solution:

Using Excel, it would be =ppmt(4%/12, 101, 300, 100000), which gives -271.30 (meaning a reduction of 271.30 against the principal).

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring math, definitions are needed. The tutor shares the definition of amortization.

Amortization schedules and amortization functions are commonly encountered in financial math. What does amortization mean?

amortization: the separation of a loan payment into two amounts:

1. the payment against principal;
2. the interest

Source:

Hewlett-Packard Business Calculator Owner’s Manual. Corvallis: Hewlett-Packard, 1988.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring high school math, you see financial word problems. The tutor gives an example.

Problem: At 12% tax, what discount will lead to paying exactly the sticker price after tax?

Solution

The final price, f, is as follows:

f = (1-discount)(1+tax)p

Where p is original price, and discount and tax are in decimals, not percent (eg, tax is 0.12 rather than 12%)

We need f=p, at tax=0.12:

p=(1-discount)(1+0.12)p

Dividing both sides by p we get

1=(1-discount)(1.12)

Then, dividing by 1.12,

0.8929 = 1-discount

Rearranging we get

discount = 1-0.8929 = 0.1071 or 10.71%.

Apparently, at 12% tax, a discount of 10.71% is needed to equate the after-tax price to the sticker price.

Cheers.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring financial math, you might often use the HP-10B. The tutor shows how easily it can apply a discount then add tax to get the final price.

Example: Imagine a handbag is regular price \$85 but is discounted by 20%. Assuming 12% sales tax, find final price using the HP-10B.

Solution:

1. Key in 85
2. Key in – 20 % =
3. Key in + 12 % =

HTH:)

Source:

Hewlett-Packard HP-10B Business Calculator Owner’s Manual. Corvallis: Hewlett-Packard, 1994.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring financial math, you might fall in love with a calculator. The tutor tells about markup on the HP-10B.

Example: Imagine you buy a product for \$35, then want to apply a 25% markup. Find the tag price using the HP-10B.

Solution:

1. Key in 35 then CST
2. Key in 25 then the orange key then MAR
3. Press PRC

HTH:)

Source:

Hewlett-Packard HP-10B Business Calculator Owner’s Manual. Corvallis: Hewlett-Packard, 1994.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring financial math, you’ll likely encounter the capable HP-10B. The tutor tells how to use its user-accessible memory.

The HP-10B seems to have 11 dedicated places to store your own numbers. The locations are at 0 to 9, plus there is the M register.

Example: On the HP-10B, store the number 65.21 in register 5.

1. Key in 65.21
2. Press the orange key
3. Press RCL
4. Press 5

To retrieve the number,

1. Press RCL
2. Press 5

HTH:)

Source:

Hewlett-Packard Business Calculator HP-10B Owners Manual. Corvallis: Hewlett-Packard, 1994.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# The tutor works a word problem to find time until market share equalization.

Imagine a relatively new device, of which there are two competing versions, A and B. (We assume that no-one owns both.) The potential market is 100 million, but at present, 20 million own A, while 12 million own B. Currently, however, B outsells A 2:1. Combined sales total 600 000 per month.

Assuming only new sales (as opposed to replacement), and only one per customer, when will ownership of B equal A? How many of each will have sold by then? What will be the total market penetration?

Solution:

Let

x=new sales of A (which means 2x=new sales of B)
t=time

We want the owned units of A to equal the owned units of B

20 000 000 + x = 12 000 000 +2x

Subtracting x and also 12 000 000 from both sides gives

8 000 000 = x

Right now, 20 000 000 people own A. So when 8 000 000 more units of A have sold, 28 000 000 will own one. During that time, 16 million units of B will sell; 12 million people own B right now. 16 million + 12 million = 28 million, the same as A will be.

At market equalization, 28 000 000 customers will own each. Therefore, 56 000 000 will own one or the other: total market penetration will be 56%.

How long will market equalization take? Of the 600 000 units selling each month, 200 000 are A (while 400 000 are B). At 200 000 units per month, the time for 8 000 000 units to sell is 8 000 000 ÷ 200 000 = 40 months.

HTH:)

Source:

Tan, S.T. Applied Finite Mathematics. Boston: PWS-KENT, 1990.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# The tutor shows a present value example on the Hewlett Packard 10B business calculator.

Example: If \$100 is received at month end for five years, at annual interest rate 3.2% compounded monthly, what is the total present value of the payments?

Solution:

1. Press the key that’s an orange rectangle, then INPUT to clear all the financial values.
2. Key the following: 100 PMT 3.2 I/YR 12 orange rectangle key PMT 0 FV 5 orange rectangle key N PV
3. Hopefully you receive the answer -5537.80
4. The negative sign just means the present value is “opposite” of the received payments: you’d have to pay 5537.80 now to receive the \$100 payments, monthly for 5 years, at 3.2% compounded monthly.

HTH:)

Source: Hewlett-Packard Business Calculator Owner’s Manual, Edition 6. Corvallis: Hewlett-Packard, 1988.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# The tutor shows an example of how to price a bond.

Example:

Imagine the following scenario: a 20-yr \$10K bond pays at 4% per year, compounded and paid semi-annually. However, realizing a present interest rate of only about 2.5%, a second buyer is happy to buy the bond for 3% yield. How much should the second buyer pay if they buy right after the interest payment at 5 years?

Solution:

Assuming the interest payment at exactly 5 years goes to the previous owner, the second buyer’s first interest payment will be at 5½ years (5 years, 6 months).

To find the purchase price, we find the present value of all the bond’s future interest payments, then its redeem value of \$10K.

##### Interest payments:

At half-year intervals, the first being at 5½ years, the last at 20 years, there will be 30 payments total. One way of seeing it: the original purchaser’s first interest received was 6 months after purchase, their last at 5 years in. Therefore, they got 10 payments. The bond pays, in total, 40 payments: 2 per year for 20 years. Therefore, the second buyer gets the other 30 payments.

Each interest payment is \$200: the interest is 4% annually, but paid and compounded semi-annually. Therefore, the interest per period is 4%/2 or 2%. 2%x10K=\$200.

The second buyer expects only 3% annually, paid and compounded semi-annually. %i is 3/2=1.5.

Here are the inputs:

First, 2nd FRQ 2nd N to clear the financial registers.

0 FV
200 PMT
1.5 %i
30 N
CPT PV

Hopefully you get the answer 4803.1676

##### \$10K redeem value:

Next, we find the present value of the \$10K redeem value, payable 15 years from today:

10000 FV
0 PMT
1.5 %i
30 N
CPT PV

Hopefully you get the answer 6397.6243.

If the second buyer wants a 3% yield for this bond, they should pay 4803.1676 + 6397.6243 = 11200.79.

HTH:)

Source:

Killip, T. Brian. Mathematics for Business: the CGA Reference Handbook. Toronto: Harcourt Brace & Company, 1993.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.