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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsCommercial ArithmeticsSimple & Compound Interest

### Compound Interest

Compound interest is made easy with the following.

maturity value in n time periods A = P (1+R)^n
=P(1+R)(1+R)(1+R)...n times
Note: R is the (interest rate in percentage)/100.

The interest is calculated on the principal for each of the time period in n. That is, the principal for the second time period is the maturity value of first time period, and so on for subsequent time periods.

Once the above is understood, the equation is easily derived.

click on the content to continue..

A borrower takes a loan from lender. The loan is for 2000 coins with 10% interest per annum for 3 years.

The interest for the first year is 2000 xx 10/100 = 200
The interest for the second year is 2000 xx 10/100 = 200
The interest for the third year is 2000 xx 10/100 = 200

There are two choices in paying the interest.
1.  The borrower can pay the interest every year, OR,
2.  the borrower can pay the maturity value at the end of 3 years.

In deciding between these two choices, which of the following is correct?

• If the interest is paid every year, then the lender can use the interest amount to make more money
• If the interest is paid every year, then the lender can use the interest amount to make more money
• there is no difference between these two forms of payments.

The answer is "If the interest is paid every year, then the lender can use the interest amount to make more money".

A borrower takes a loan from a lender. The loan is for 2000 coins with 10% interest per annum for 3 years.

The interest for the first year is 2000 xx 10/100 = 200
The interest for the second year is 2000 xx 10/100 = 200
The interest for the third year is 2000 xx 10/100 = 200
If, at the end of first year, the interest 200 coins is paid to lender, then the lender can loan the interest and earn additional interest on that loan too.

If the borrower wants to pay back the principal and the interest only after the 3 year period, then which of the following is correct?

• borrower should pay the 2000 coins and the 600 coins interest
• borrower should compensate on the additional interest the lender would make on the interest from first year
• borrower should compensate on the additional interest the lender would make on the interest from first year

The answer is "borrower should compensate on the additional interest, the lender would make on the interest from first year".

A borrower takes a loan from a lender. The loan is for 2000 coins with 10% compound interest per annum for 3 years.

The interest for the first year is 2000 xx 10/100 = 200
The principal for the second year is the principal and interest, 2000 + 200 = 2200

The interest for the second year is 2200 xx 10/100 = 220
The principal for the third year is the principal of second year and interest, 2200 + 220 = 2420

The interest for the third year is 2420 xx 10/100 = 242
The maturity value in the third year is, 2420 + 242 = 2662

This interest calculation compensates the lender for the additional interest she would earn in lending the interests from first and second years.

A customer deposits 2000 coins in a bank. The interest is 10% per annum for 3 years.

The interest for the first year is 2000 xx 10/100 = 200
The interest for the second year is 2000 xx 10/100 = 200
The interest for the third year is 2000 xx 10/100 = 200

There are two choices in paying the interest.
1.  The bank can pay the interest every year, OR,
2.  the bank can pay the maturity value at the end of 3 years.

In deciding between these two choices, which of the following is correct?

• If the interest is paid every year, then the customer can deposit the interest which will provide additional interest
• If the interest is paid every year, then the customer can deposit the interest which will provide additional interest
• there is no difference between these two forms of payments.

The answer is "If the interest is paid every year, then the customer can deposit the interest which will provide additional interest".

A customer deposits 2000 coins in a bank. The interest is 10% per annum for 3 years.

The interest for the first year is 2000 xx 10/100 = 200
The interest for the second year is 2000 xx 10/100 = 200
The interest for the third year is 2000 xx 10/100 = 200

If, at the end of first year, the interest 200 coins is paid to the customer, then the customer can deposit the interest and earn interest on that deposit too.

If the bank wants to pay back the principal and the interest only after the 3 year period, then which of the following is correct?

• bank should pay the 2000 coins and the 600 coins interest
• bank should compensate on the additional interest the customer would make on the interest from first year
• bank should compensate on the additional interest the customer would make on the interest from first year

The answer is "bank should compensate on the additional interest the customer would make on the interest from first year".

A customer deposits 2000 coins in a bank. The compound interest is 10% per annum for 3 years.

The interest for the first year is 2000 xx 10/100 = 200
The principal for the second year is the principle and interest, 2000 + 200 = 2200

The interest for the second year is 2200 xx 10/100 = 220
The principal for the third year is the principle in second year and interest, 2200 + 220 = 2420

The interest for the third year is 2420 xx 10/100 = 242
The maturity value in the third year is, 2420 + 242 = 2662

This calculation compensates the customer for the additional interest she would earn in depositing the interests from first and second years.

Which of the following is a meaning for the word "compound"?

• made up of several parts
• made up of several parts
• a wall with electric fencing

The answer is "made up of several parts".

What is the term used to refer "interest that accumulates into principal every time period"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "compound interest".

Compound Interest : At the end of every interest period, the interest is added into principal is compound interest. The interest for the next period is paid on the revised principal.

A borrower takes a loan of 2000 coins at 12% per annum interest. The interest is compounded every month.

Note that the interest rate is given for yearly.
But the compounding of interest is for every month.

What is the interest per month?

• 12% monthly
• 12//12 monthly which is 1%
• 12//12 monthly which is 1%

The answer is "1%"

A borrower takes a loan of 2000 coins at 12% per annum interest. The interest is compounded every month.
The interest for the compounding interval (1 month) is 1%.
The interest for the first interval =2000 xx 1/100 =20
The interest for the second interval =2020 xx 1/100 = 20.20
The interest for the third interval =2040.20 xx 1/100 =20.402

Which of the following is a meaning for the word "interval"?

• a time gap between two events
• a time gap between two events
• not touched and in full

The answer is "a time gap between two events".

What is the term used to refer "a time gap between two events"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "interval".

Which of the following is a meaning for the word "frequency"?

• parallel to a line
• rate at which something occur repeatedly
• rate at which something occur repeatedly

The answer is "rate at which something occur repeatedly".

What is the term used to refer "rate at which something occur repeatedly"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "frequency".

Compounding Interval : The time period for which the interest is calculated and added to the principal.

Compounding Frequency : The compounding interval given as a frequency form, like monthly, quarterly, annual, etc.

Students may find it difficult to memorize all the formulas for compound interest. This is listed for reference, but in the next page, these are explained. No need to memorize any of them.

Principal P
Interest Rate R
Number of time periods n
Maturity value or amount A

Maturity value A = P (1+R//100)^n
Principal P = A // (1+R//100)^n

One need not memorize any formulas. Quickly follow through the story to recall the formula on the fly.

•  Interest is calculated as percentage of the principal (Interest I=PR//100 for every time period. Note: only the first interest duration is considered.)

•  Interest at the end of first time duration is added to the principal. (A=P + PR/100 =P(1+R//100))

•  The borrower has to return the principal and the interest, which together is the maturity value.

Principal for the second time period P_1 = P

Maturity Value in first time period A_1 = Principal P+  Interest P xx R// 100

Principal for the second time period P_2 = Principal P+  Interest P xx R// 100 =P(1+R//100)

Maturity Value in second time period A_2 = Principal P_2+  Interest P_2 xx R// 100=P_2(1+R//100) =P(1+R//100)^2

maturity value in n time periods A = P (1+R//100)^n

There are 4 variables (A, P, R, n) in this equation. In a problem, 3 of these 4 variables are given and this formula is a form of equation of one variable (algebra) to solve for the unknown variable.

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