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QUESTION 6 A loan of $10 000 has interest charged on a reducing balance at 6% p.a. compounding quarterly with quarterly repayments of $700. The balance after 6 months is (A) $8696.75 (B) $8891.75 (C) $8900.00 (D) $9794.00
QUESTION 15 The graph shows the value of three different annuities over time. 3000 —e— Annuity 1 --%-- Annuity 2 2500 — 4 — Annuity 3 2000 1500 1000 Value of investment ($) 500 Number of terms Which of the following statements gives a plausible explanation for the different values after seven terms? (A) (B) ©) (D) Annuity 1 and Annuity 2 have higher regular deposits than Annuity 3. Annuity 1 and Annuity 2 have shorter interest terms than Annuity 3. Annuity 2 and Annuity 3 have a lower initial value than Annuity 1. Annuity 2 and Annuity 3 have higher interest rates than Annuity 1.
QUESTION 20 (4 marks) Determine the monthly repayment on a $350 000 home loan over 25 years with 6.5% p.a. fixed interest compounded monthly.
QUESTION 25 (5 marks) A financial institution offers two investment options: Option 1: 7% p.a. compounding quarterly Option 2: 6.8% p.a. compounding monthly Use the effective interest rate formula to determine the option that will provide the better return.
QUESTION 7 (7 marks) A couple saved for their retirement by making the same monthly payments for 20 years into an account that earned 4.2% p.a. compounded monthly. At the age of 65 the couple retired and used all their savings to purchase a perpetuity with an interest rate of 5.76% p.a. compounded monthly paying $3600 each month. How much did they save each month to prepare for their retirement?
QUESTION 15 Which of the following investment options gives the best return? (A) 5.93% p.a. compounding daily (B) 5.95% p.a. compounding monthly (C) 5.97% p.a. compounding quarterly (D) 5.99% p.a. compounding six-monthly
QUESTION 17 (4 marks) Determine the monthly repayment on a reducing balance loan of $720 000 at 4.8% p.a. over 25 years. Give your answer to the nearest dollar.
QUESTION 22 (4 marks) Rosa borrowed $32 000 as a reducing balance loan at 4.8% p.a. compounding monthly with monthly repayments of $278. How much will Rosa owe after 2 months to the nearest cent?
QUESTION 3 (5 marks) Jo contributes $2500 per quarter to an annuity earning 3.6% p.a. compounding quarterly. At the end of 4 years Jo makes a one-off extra contribution of $10 000 and continues with the regular quarterly contributions. Determine the value of the annuity at the end of 6 years to the nearest dollar.
QUESTION 4 (6 marks) The graph shows two investment models. Model 1 is compounding annually while Model 2 increases linearly by $126 per year. Model 1 2750 __- Model 2 Amount ($) 2020 2038 Year Determine the difference between the two investment strategies in 2030 to the nearest dollar.
QUESTION 17 (4 marks) An investment of $50 000 that compounds interest monthly is modelled by the recurrence relation A . 1=1.003754 where Ay =50 000. a) What would be the advertised interest rate per annum compounding monthly? [2 marks] b) How many months would it take for the value of the investment to exceed $51 000? [2 marks]
QUESTION 25 (5 marks) A couple borrow money to complete home renovations. Their bank has loaned the amount at 2.4% p.a. compounding monthly with repayments of $993.14 each month for 15 years. a) Determine the amount of money borrowed. [3 marks] b) Write a recurrence relation for the amount owing after n» months. [2 marks]
QUESTION 2 (5 marks) Tam deposits a fixed amount at the end of each month into an account paying 8.6% p.a. compounding monthly. From an initial zero balance she accumulates $51 343.85 in four years. A financial planner has advised Tam that she would have been at least $3000 better off if she had instead deposited half of the fixed amount at the end of each fortnight into an account paying 7.9% p.a. compounding fortnightly. Evaluate the reasonableness of this advice.
QUESTION 11 An annuity with an initial zero balance has $500 deposited at the end of every month. The annuity earns 4.8% p.a. interest compounding monthly. At the end of the fourth month the balance is closest to (A) $2002 (B) $2008 (C) $2012 (D) $2014
QUESTION 12 A reducing balance loan with an initial balance of $6000 is modelled by the recurrence relation Anal = [ + “) A — 400 where n is the number of months. The loan balance at the end of two months is closest to (A) $5100 (B) $5200 (C) $5215 (D) $5230
QUESTION 17 (4 marks) Terome paid a $50 000 deposit on a house valued at $570 000 and borrowed the remainder as a reducing balance loan at 6.6% p.a. compounding monthly. Determine the monthly repayment required to pay off the loan over 25 years.
QUESTION 19 (4 marks) Ngarra compares two investment options and decides option A will provide the better return. ¢ Option A: 5.60% p.a. compounding monthly ¢ Option B: 5.62% p.a. compounding quarterly Use the effective annual rate of interest formula to evaluate the reasonableness of Ngarra’s decision.
QUESTION 7 (5 marks) Five years ago a retiree invested $100 000 in a compound interest account earning 3.8% p.a. compounding monthly. They now intend to use the balance of the account to begin a perpetuity that will return 4% p.a. compounding annually and pay them $6000 each year. Provide advice to the retiree about whether their compound interest investment is large enough to finance the perpetuity.
QUESTION 2 The graph below shows the relationship between the amount owed and time taken to repay a reducing balance loan. 140 000 120 000 o 000e 000 00 c ..... 100 000 T 80 000 60 000 Amount owed ($) 40 000 20 000 0 20 40 60 80 100 120 140 160 180 Time (months) The owed amount will be reduced to half the original amount borrowed in (A) 60 months. (B) 81 months. (C) 112 months. (D) 162 months.
QUESTION 13 For a personal loan of $350 a payment of $60 is made after interest is added each month. The following recurrence relation shows the remaining balance at the end of consecutive months. The recurrence relation is Anv = 1.02434 - 60 The remaining balance after two months is (A) $191.73 (B) $242.81 (C) $245.76 (D) $298.51
QUESTION 17 A reducing balance loan of $12 000 was taken out at 10.5% per annum with interest calculated monthly for five years. Determine the monthly repayment required to pay off the loan. (A) $152.93 (B) $162.18 (C) $25793 (D) $267.18
QUESTION 19 An investment of $10 000 is made at an interest rate of 7.5% per annum compounding half yearly. The number of years it will take for the value of the investment to exceed $18 000 is (A) 7 (B) 8 C) 15 (D) 16
QUESTION 21 (4 marks) To provide herself with a regular income at retirement Mary invests in an annuity worth $270 000 at 3.5% per annum compounding monthly for 20 years. Calculate how much income she will receive each month.
QUESTION 4 (3 marks) You have a savings account with an interest rate of 2.4% per annum paid quarterly. Your bank makes you a new offer. You are entitled to either an increase in the interest rate of 0.5% per annum or to your current interest paid monthly. Determine which option is the most profitable.
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