Topicmcb552cef44903929_1528449000663_0Topic

Compound interest

Levelmcb552cef44903929_1528449084556_0Level

Third

Core curriculummcb552cef44903929_1528449076687_0Core curriculum

I. Real numbers. Student:
8. uses the properties of exponentiation (powers) and radication (roots) in practical applications, including the calculation of compound interest, investment profits and loan costs.

Timingmcb552cef44903929_1528449068082_0Timing

45 minutes

General objectivemcb552cef44903929_1528449523725_0General objective

To interpret, analyse and manipulate information presented in both mathematical and popular science texts, as well as in the form of graphs, diagrams, tables.

Specific objectivesmcb552cef44903929_1528449552113_0Specific objectives

1) To communicate in English; develop mathematics and basic scientific, technical and IT competences, shape and develop learning skills.

2) Calculating interest rates on deposits.

3) Applying compound interest in calculations.

Learning outcomesmcb552cef44903929_1528450430307_0Learning outcomes

The student:

- calculates interest rates on deposits,

- uses compound interestcompound interestcompound interest in calculations.

Methodsmcb552cef44903929_1528449534267_0Methods

1) Task‑based competition.

2) Case study.

Forms of workmcb552cef44903929_1528449514617_0Forms of work

1) Individual work.

2) Group work.

Lesson stages

Introductionmcb552cef44903929_1528450127855_0Introduction

Students were supposed to prepare for the lesson at home and review their current knowledge related to the calculation of percentages.

The lesson begins with a short, individual task competition. The first 3 students who solve the tasks correctly will be rewarded with the best grades.

Competition - task 1
Calculate 23% of the number 2700.
Answer: 621.

Competition - task 2
14% of a certain number equals 112. What is this number?
Answer: 800.

Competition - task 3
What percentage of the number 1200 is the number 630?
Answer. 52.5%.

The teacher summarizes the results of the competition. Clarifies the doubts.

Proceduremcb552cef44903929_1528446435040_0Procedure

The teacher informs that the aim of the lesson is to develop skills related to the calculation of interest rates on bank depositsbank depositsbank deposits.

Students, working in groups, analyze the illustration showing the interest rateinterest rateinterest rate on bank depositsbank depositsbank deposits. They formulate applicable conclusions.

[INTERACTIVE ILLUSTRATION]

Conclusion
It is more beneficial to put money in a bank where the capitalization of interest is carried out more often than once a year, than in a bank where the capitalization of interest is carried out once a year.mcb552cef44903929_1527752263647_0Conclusion
It is more beneficial to put money in a bank where the capitalization of interest is carried out more often than once a year, than in a bank where the capitalization of interest is carried out once a year.

The formula for calculating the capital accumulated on the deposit with the aid of compound interest.mcb552cef44903929_1527752256679_0The formula for calculating the capital accumulated on the deposit with the aid of compound interest.

$K_0$ - initial capitalinitial capitalinitial capital 
$K_n$ - capital accumulated after capitalization periods 
$n$ - the number of capitalization 
$p\%$ - interest on the deposit in the period in which the capitalization takes place

Students use the formula they have learned to solve tasks.

Task
Mr. Kowalski submitted to the bank PLN 6000 for four years on compound interestcompound interestcompound interest. What amount will he have on his account after this period, if the interest rateinterest rateinterest rate in the bank is 10% per annum, and the interest is capitalized every three months?
Answer. PLN 8907.03.

Task
How much money should I put into the bank for the compound interestcompound interestcompound interest so that at 10% interest rateinterest rateinterest rate and the annual capitalization period, after 10 years I receive PLN 10,000?
Answer. PLN 6,755.60

Task
What capital will an 18‑year‑old have at his disposal if his parents, since his birth, located PLN 500 each year in the bank? The interest rateinterest rateinterest rate was 6% per annum, and the interest was capitalized every year.
Answer. approximately PLN 14 952.83

An extra task
Banks A, B, C, D offer the following conditions for two‑year deposits.

Bank A - 5.4% per annum, interest capitalized on a monthly basis.
Bank B - 5.5% per annum, interest capitalized every quarter.
Bank C - 5.6% per annum, interest capitalized every six months.
Bank D - 5.7% per annum, interest capitalized every year.

Which of the above banks offers the most favorable conditions?
Answer. Bank C.

Lesson summarymcb552cef44903929_1528450119332_0Lesson summary

Students do revision exercises. Together, they formulate a rule to remember.

- The compound interestcompound interestcompound interest is the interest rateinterest rateinterest rate on the cash contribution. It means that interest for a given saving period is added to the contribution, i.e. they are subject to capitalization. This causes an increase in capital in the subsequent saving period.

Selected words and expressions used in the lesson plan

bank depositsbank depositsbank deposits

capitalisation of interestscapitalisation of interestscapitalisation of interests

compound interestcompound interestcompound interest

deposit interest ratesdeposit interest ratesdeposit interest rates

final capitalfinal capitalfinal capital

initial capitalinitial capitalinitial capital

interest rateinterest rateinterest rate