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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 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 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 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 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 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 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.
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