1. Credit and borrowing Cambridge University Press1  G K Powers 2013

Flat-rate loans Exercise 1A 14. A truck is advertised at $ It can be bought on terms for a 20% deposit and repayments of $276 per week for 3 years. Assume there are 52 weeks in the year. a. What is the deposit? b. Calculate the total cost of the truck if bought on these terms. c. What is the total interest paid? d. What is the flat interest rate for the loan, correct to one decimal place? 2 Cambridge University Press  G K Powers 2013

Solution 14. d. 3 a. b. c. Cambridge University Press  G K Powers 2013

Flat-rate loans Exercise 1A 15. Determine the flat rate of interest charged on a painting that has a cash price of $7500. The painting was purchased on terms with a 20% deposit and the balance to be paid at $370 per month for 2 years. 4 Cambridge University Press  G K Powers 2013

Solution Cambridge University Press  G K Powers 2013

Flat-rate loans Exercise 1A 16. Grace takes a loan of $ over 60 months for a swimming pool. The repayment rate is $ per month. a. How much will Grace pay back altogether? b. What is the flat interest rate per annum for the loan, correct to one decimal place? c. Grace would like to increase the loan to $ to landscape the pool. What would be her monthly repayment assuming the same time period and flat interest rate? Answer correct to the nearest cent. 6 Cambridge University Press  G K Powers 2013

Solution 16. b. Monthly repayment is $ a. c. Cambridge University Press  G K Powers 2013

Flat-rate loans Additional question Willow brought a home theatre system for $2500. She pays it off monthly over 2 years at an interest rate of 12.5% per annum flat. How much per month will she pay? 8 Cambridge University Press  G K Powers 2013

Solution Repayment required is $130 per month. 9 Cambridge University Press  G K Powers 2013

Table of loan repayments Exercise 1B 6. Dylan borrowed $ for an investment property. The interest rate is 10% p.a. and he makes monthly repayments of $2300. Construct a table of home loan repayments for the first two months to answer the following questions. a. How much interest was paid in the first month? b. What is the balance owing after one month? c. How much has the principal been reduced during the first month? d. How much interest was paid in the first two months? e. What is the balance owing after two months? f. How much has the principal been reduced during the first two months? 10 Cambridge University Press  G K Powers 2013

Solution 6. d. Second month 11 b. a. c. Cambridge University Press  G K Powers 2013

Solution f. e. Cambridge University Press  G K Powers 2013

Table of loan repayments Exercise 1B 7. Charlotte borrowed $ for an inner city apartment. The interest rate is 8% p.a. and she makes fortnightly repayments of $1600. Construct a table of home loan repayments for the first three fortnights. a. What is the balance owing after the first fortnight? b. How much interest was paid after the first fortnight? c. How much has the principal been reduced during the first fortnight? d. What is the balance owing after three fortnights? e. How much interest was paid in the three fortnights? f. How much has the principal been reduced during the first three fortnights? 13 Cambridge University Press  G K Powers 2013

Solution a. b. c. Cambridge University Press  G K Powers 2013

Solution 7. d. Second month Third month 15 Cambridge University Press  G K Powers 2013

Solution 7.e. 16 f. Cambridge University Press  G K Powers 2013

Table of loan repayments Additional question Ben has borrowed $ at an interest rate of 6.24% per annum compounded monthly. The repayments have been set at $680 per month. a. What is the interest charged at the end of the first month? b. Calculate the balance at the end of the first month. 17 Cambridge University Press  G K Powers 2013

Solution Balance at the end of the first month is $ Interest charged is $ a. b. Cambridge University Press  G K Powers 2013

Future value formula Exercise 1C 12.How much more interest is earned on a $ investment if the interest at 8% p.a. is compounded quarterly over 6 years, than if simple interest of 8% p.a. is earned over the same time? 19 Cambridge University Press  G K Powers 2013

Solution Cambridge University Press  G K Powers 2013

Future value formula Exercise 1C 13.Mikayla invests $ for 10 years at 6% p.a. interest compounded quarterly. Abby also invests $ for 10 years, but her interest rate is 6% p.a. compounded monthly. a. Calculate Mikayla’s investment at maturity. b. Show that the compounded value of Abby’s investment is greater than the value of Mikayla’s investment. c. Explain why Abby’s investment is worth more than Mikayla’s investment. 21 Cambridge University Press  G K Powers 2013

Solution 13. c. Interest is compounded monthly compared with quarterly. 22 a. b. Cambridge University Press  G K Powers 2013

Future value formula Additional question Jake has $ to invest for 3 years. A financial institution offers Jake a choice between two rates: 5.15% p.a. compounded half-yearly and 5.1% p.a. compounded monthly. Which is the better investment for Jake? Give a reason for your answer. 23 Cambridge University Press  G K Powers 2013

Solution First investment Second investment 5.1% p.a. compounded monthly is the better investment. 24 Cambridge University Press  G K Powers 2013

Comparing loans Exercise 1D 5. A finance company advertises home loans with an interest rate of 9% p.a. compounded monthly. What is the effective interest rate over a 12-month period? Answer correct to two decimal places. 25 Cambridge University Press  G K Powers 2013

Solution 5. Effective interest rate is 9.38% p.a. 26 Cambridge University Press  G K Powers 2013

Comparing loans Exercise 1D 6. Lily and Jacob would like to borrow $ for a home to be repaid in equal monthly instalments of $1800 over 30 years. a. How much is paid on the loan for one year? b. Determine the total amount to be repaid on the loan. c. Calculate the total interest payment. d. What is the equivalent annual flat rate of interest? Answer correct to one decimal place. e. What is the effective interest rate if the annual interest rate is compounded monthly? Answer correct to one decimal place. 27 Cambridge University Press  G K Powers 2013

Solution 6. d. 28 a. b. c. Cambridge University Press  G K Powers 2013

Solution 6. Effective interest rate is 7.7% p.a. 29 e. Cambridge University Press  G K Powers 2013

Comparing loans Additional question Calculate the effective interest rate given an interest rate of 15% p.a. with interest compounded half-yearly. Answer correct to two decimal places. 30 Cambridge University Press  G K Powers 2013

Solution Effective interest rate is 15.56% p.a. 31 Cambridge University Press  G K Powers 2013

Credit cards Exercise 1E 12. Sarah and Joshua each use their credit cards to buy holiday packages to Adelaide. The cost of the package is $1700 for each person. a. The charge on Sarah’s credit card is 0.9% compound interest per month on the unpaid balance. Sarah pays $800 after one month and another $500 the next month. How much does she still owe on her credit card? b. The charge on Joshua’s credit card is no interest in the first month, and 1.4% compound interest per month on any unpaid balance. Joshua pays $800 after one month and another $500 the next month. How much does he still owe on his credit card? 32 Cambridge University Press  G K Powers 2013

Solution 12. a. First month Second month 33 Cambridge University Press  G K Powers 2013

Solution 12. b. First month – interest free Second month 34 Cambridge University Press  G K Powers 2013

Credit cards Exercise 1E 13.Emily’s August credit card statement shows an opening balance of $1850, a purchase of $2450 on August 5, and another purchase of $55 on August 14. The minimum payment is 3% on the closing balance. The initial credit charge is 1.6% compounding per month of any amount outstanding. a. What is closing balance on this credit card for August? b. Calculate the amount of interest charged for the month of August. c. What is the minimum payment, to the nearest cent, required for August? d. What is the opening balance for October if Emily paid the minimum payment in September for interest charged in August and made no purchases in September? 35 Cambridge University Press  G K Powers 2013

Solution a. b. c. d. Cambridge University Press  G K Powers 2013

Credit cards Additional question A bank charges % interest per day on the amount owing on a credit card. What is the interest charged in four weeks on a balance of $1400? 37 Cambridge University Press  G K Powers 2013

Solution Interest charged is $ Cambridge University Press  G K Powers 2013