1. Credit and borrowing  Calculate the principal, interest and repayments for flat-rate loans  Calculate the values using a table of home loan repayments  Calculate future value and present value  Compare different options for borrowing money  Calculate credit card payments, interest charges and balances Cambridge University Press 1  G K Powers 2013

Flat-rate loans I – Interest (simple or flat) to be paid for borrowing the money P – Principal is the initial amount of money borrowed r – Rate of simple interest per period expressed as a decimal n – Number of time periods A – Amount or final balance Flat-rate loans use simple interest. Simple interest is calculated on the initial amount borrowed or the principal. Cambridge University Press2  G K Powers 2013

Example 1.Chelsea applied for a flat-rate loan of $ at 7% per annum simple interest. She plans to repay the loan after two years and six months. a.How much interest will be paid? b.What is the total owing at the end of the two years and six months? 2.Matthew borrowed $ at 11% p.a. How many years did it take to pay off the loan if the total simple interest was $3300? Cambridge University Press 3  G K Powers 2013

Solution 1. a.b. Simple interest owed is $ Amount owed is $ It takes Matthew 2.5 years to pay off the loan. Cambridge University Press4  G K Powers 2013

Loan repayments A loan repayment is the amount of money to be paid at regular intervals over the time period. The interval is often fortnightly or monthly. Loan repayment = Total to be paid ÷ Number of repayments Example Belinda wishes to buy an oven priced at $1550. She chooses to buy it on terms by paying a 10% deposit and borrowing the balance. Interest is charged at 11.5% p.a. on the amount borrowed. Belinda makes fortnightly repayments over 3 years. Calculate her fortnightly repayments. Cambridge University Press 5  G K Powers 2013

Solution Fortnightly repayments are $ Cambridge University Press 6  G K Powers 2013

Table of loan repayments  The interest on a home loan is often calculated per month on the amount of money owing and repayments are made per month.  The balance owing after each month becomes the new principal for the next month.  Each calculation results in a smaller amount of interest and is called reducible interest. These calculations are often displayed in a table. Cambridge University Press7  G K Powers 2013

Example Examine the table of home loan repayments. 1.What is the principal at beginning of the third month? 2.Calculate the interest charged for the third month. 3.How much money is owed at the beginning of the fourth month? Cambridge University Press8  G K Powers 2013

Solution $ Cambridge University Press9  G K Powers 2013

Future value formula FV – Future value of the loan or amount (final balance) PV – Present value of the loan or principal r – Rate of simple interest per period expressed as a decimal n – Number of compounding time periods I – Interest (compounded) earned for the use of money Cambridge University Press10  G K Powers 2013

Example 1.Roshan invests $5 000 over 5 years at a compound interest rate of 6.5% p.a. a.Calculate the future value after 5 years. Answer correct to the nearest cent. b.Calculate the interest earned after 5 years. Answer correct to the nearest cent. 2.Calculate the present value of an annuity to accumulate a future value of $ at the end of 3 years at 7.5% p.a. compound interest. Give your answer correct to the nearest cent. Cambridge University Press11  G K Powers 2013

Solution a.b. Future value is $ Interest earned is $ Present value is $ Cambridge University Press12  G K Powers 2013

Comparing loans  Comparing loans and making the best choice is not simply about choosing a loan with the lowest interest rate. Borrowers need to consider flexibility, fees and the rate.  Flexibility is the ability to redraw money and make extra repayments.  Comparison rate calculators are available on the internet to compare loans. Cambridge University Press13  G K Powers 2013

Effective interest rate The effective interest rate is an equivalent interest rate if compounding happened annually. The effective interest rate is a single rate that takes into account different rates and time periods. E – Effective rate of interest per annum as a decimal r – Rate of interest per compounding period expressed as a decimal n – Number of compounding time periods per annum Cambridge University Press 14  G K Powers 2013

Example Calculate the effective annual interest rate of a home loan with an interest rate of 6.75% p.a. compounded monthly. Give your answer as a percentage correct to two decimal places. Cambridge University Press 15  G K Powers 2013

Solution Effective interest rate is 6.96%. Cambridge University Press16  G K Powers 2013

Credit cards A – Amount owing on the credit card P – Principal is the purchases made on the credit card plus the outstanding balance r – Rate of interest per compounding period expressed as a decimal n – Number of compounding time periods I – Interest (compounded) earned for the use of money Credit cards are used to buy goods and services and pay for them later. The time you will not be charged interest on your purchases is called the interest-free period. If payment is not received when the statement is due then interest is paid. Cambridge University Press 17  G K Powers 2013

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Example 1.Richard has a credit card with an compound interest rate of 22% p.a. and no interest-free period. Richard used the credit card to pay for a phone costing $ He paid the credit card account 14 days later. What is the total amount he paid for the phone including interest? 2.Gabriel received a new credit card with no interest-free period and a daily interest rate of 0.05% compound. She used her credit card to purchase clothing for $350 and petrol for $60 on the 20th March. This amount stayed on the credit card for 25 days. What is the total interest charged? Cambridge University Press19  G K Powers 2013

Solution Total paid is $ Interest charged is $5.16. Cambridge University Press20  G K Powers 2013