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AIM

AND OBJECTIVES

Aim: Simple and Compound Interests

Objectives: At the end of the lesson, the students should be able to:

Define interest rate and differentiate between the two fundamental types.
Apply simple and compound interests to different construction and financial scenarios.
Discuss a range of techniques for assessing the cost of borrowing.

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LEARNING OUTCOMES AND

ASSESSMENT CRITERIA

P4 Discuss a range of techniques for assessing the cost of borrowing.

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INTRODUCTION

Interest, in financial terms, is the cost of borrowing money or the compensation received for lending funds.
It is a critical component of the financial system and plays a central role in various financial transactions.
When an individual, business, or government borrows money, they typically pay interest to the lender as compensation for the use of those funds. The interest rate is the fee associated with this borrowing.
Interest is proportional to the amount of money loaned or borrowed. That is, a £10,000 loan will earn a different interest amount than a £2,000 loan.

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INTRODUCTION

Conversely, when individuals or institutions deposit their money in savings accounts, certificates of deposit (CDs), or other financial instruments, they receive interest as compensation for lending their money to the financial institution.
Interest calculations depend on the duration for which the money is borrowed or lent, represented by the time period. The longer the money is involved, the more interest accrues.
If £100.00 earns £10.00 over a year, then the interest rate in this case is £10.00 / £100.00 = 0.10, or 10% per year.
Interest is typically expressed as a percentage of the principal amount (the initial sum of money) and is calculated over a specified period, known as the interest rate.

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FACTORS THAT INFLUENCE INTEREST RATE

Global economic conditions and financial markets affecting the inflation rate, etc.
Investor Confidence; The stability of the market where the money will be used.
The level of competition among lenders,
Government spending, taxation, and borrowing.
Borrower's Creditworthiness.
The degree of investment risk.

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SIMPLE AND COMPOUND INTERESTS

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WORKED EXAMPLE 1

You ask your sister to lend you the £10,000, which you will pay back at the end of 3 years. He agrees to allow you to pay simple interest at 10% interest rate, as a concession to one of his favourite family members. How much money will you have to pay back?

Year
0 (now)			10,000
1	10,000	10,0000.10 1 = 1,000	11,000
2	10,000	10,0000.10 2 = 2,000	12,000
3	10,000	10,0000.10 3 = 3,000	13,000

Alternatively,

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COMPOUND INTERESTS

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WORKED EXAMPLE 2

You ask the bank to lend you £10,000 for three years instead of your sister. They agree to allow you to pay compound interest at 10% interest rate. How much money will you have to pay back?

Year
0 (now)		10,000
1	10,000	11,000
2	10,000	12,100
3	10,000	13,310

Alternatively,

Refer to the provided ‘Compound Interest Calculator’ for different scenario.

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ANNUAL PERCENTAGE RATE (APR)

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ANNUAL EQUIVALENT RATE (AER)��ANNUAL PERCENTAGE YIELD (APY)

Annual Equivalent Rate (AER): the interest or return earned on investments, taking into account how often interest is paid on a simple interest basis.
Annual Percentage Yield (APY): the interest or return earned on investments on a compound basis. This is a better indication of returns than AER if you do not intend to make any withdrawals.
Interest can be compounded annually, semi-annually, quarterly, monthly, daily, etc (Fernando, 2023). The more frequent the compounding, the more rapidly the balance will grow.
See: https://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

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COMPOUNDING INTEREST PERIODS

Investments: The majority of investment instruments, such as savings accounts and equities, operate on the principle of compound interest. Notably, bonds and gilts are exceptions, as they offer simple interest returns.
Borrowings: Simple interest finds common application in personal loans, car loans, and various forms of short-term consumer loans. In contrast, credit cards and student loans employ compound interest, which implies that the debt can grow rapidly when not promptly repaid.
Mortgage Dynamics:

Traditional repayment mortgages utilise compound interest, with monthly payments and potential over-payments contributing to the reduction of the outstanding balance, consequently lessening the payable interest.

Interest-only mortgages rely on simple interest, which accrues monthly on the borrowed amount, with the principal being repaid separately as a lump sum at the conclusion of the mortgage term.

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PRACTICAL APPLICATIONS

Take simple interest loans.
Take loans with low interest rates.
Use loans that allow early repayment without penalty.
Deal with more expensive debts (high interest rates, debts utilising compounding interest).
Keep your investment period longer to maximise the benefit of compound interest.
Hold investment gains in an Individual Savings Account (ISA), Self Invested Personal Pension (SIPP) and Junior ISA to avoid income tax.
Hold investment gains in Enterprise Investment Scheme (EIS), Seed Enterprise Investment Scheme (SEIS), Social Investment Tax Relief (SITR) and ISAs to avoid paying capital gains tax of up to 28%.
Reinvest dividends or income: e.g. accumulated funds.

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SELF-ASSESSMENT TASK

1. Discuss at least any THREE techniques for assessing the cost of borrowing. Relate you discussion to funding of construction projects

Hint: present value approach, simple interest, compound interest, Annual Percentage Rate (APR), variable vs. fixed rates, loan amortization schedule, comparative shopping, etc.

2. Find the interest on a used car loan of £5,000 at a simple interest rate of 6% for a period of 3 years.

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SELF-ASSESSMENT TASK

3. A company is considering starting a new product line. The new product line requires the installation of new machines and equipment. For this purpose, company wants to borrow money by issuing bonds of £16,000 for 10-year period. The interest on these bonds is to be paid at a rate of 7% per year.

Compute the amount of interest to be paid to bondholders over 10-year period:

• if the simple interest is charged.

• if the interest is compounded annually.

4. Mr. Arman borrowed £6,000 from his friend to pay for remodelling work on his house. He repaid the loan 2 years later with simple interest at 5%.

His friend then invested all the money in a 10-year investment portfolio at 7% compounded yearly. How much will his friend have at the end of the 10 years?

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REFERENCES/BIBLIOGRAPHY

Fernando, J. (2023) The power of compound interest: calculations and examples. Available at: https://www.investopedia.com/terms/c/compoundinterest.asp (Accessed: 03 November 2023).
Groves, J. and Pratt, K. (2023) Understanding compound interest. Available at: https://www.forbes.com/uk/advisor/investing/understanding-compound-interest/#:~:text=Duration%3A%20the%20length%20of%20time,compounded%20daily%2C%20monthly%20or%20annually. (Accessed: 03 November 2023).
Hore, A. V., Kehoe, J. G., McMullan, R. and Penton, M. R. (1997) Construction 1 – management, finance, measurement. Hampshire: Macmillan Press LTD.
Johnson, J. (2023) Annual percentage rate (APR): what is it and how does it work? Available at: https://www.quickenloans.com/learn/apr#:~:text=The%20APR%20Formula,365%20and%20again%20by%20100. (Accessed: 03 November 2023).
Niesen, J. (2012) Maths 510: Financial mathematics I. Available at: https://www1.maths.leeds.ac.uk/~jitse/math1510/notes-all.pdf (Accessed: 24 October 2023).
Peterson, A. (2023) How to avoid capital gains tax: key considerations and strategies. Available at: https://www.growthcapitalventures.co.uk/insights/blog/how-to-avoid-capital-gains-tax-uk (Accessed: 03 November 2023).