Annuity - Future value tables

Answer the following questions using the table elsewhere when required:

Interest factors.	1. Assume deposits are made into an annuity account of $1 at the end of each period. The interest rate is 5% per period. At the end of period 1 $1 is deposited. At the end of period 2, interest is paid on that deposit and then a second deposit of $1 is made. (i) Using simple interest calculations, show that the amount in the annuity fund after the second deposit is $2.05. (ii) Continue this pattern of adding interest and then making a $1 deposit for 3 more periods. Show that after 5 deposits you have $5.53 in the fund. (iii) Compare your answers with the relevant value for the interest factors in the future table included elsewhere.
	2. Use the table below to determine the interest factor for 13 periods at an interest rate of 12%. Interpret this value by using an example.
Find the future value of an annuity.	3. What is the future value of an investment of $3,000 at the end of each period at 3% per period for 20 periods? Answer.26.8704×3,000 = $80,611.20
	4. What is the future value of an annual investment of $5,500 at the end of each year for 15 years at 5% p.a.? Answer.27.1521×5,500 = $149,336.55
	5. A deposit is made into an investment account of $10,000 each six months. The account pays 8% p.a. What is the future value of the annuity after 12 years? Answer.39.0826×10,000 = $390,826
	6. Ellen makes deposits of $450 at the end of each six months (when she has saved up her earnings from her part time job) into her Super Savings account. That account pays an amazing 12% p.a. interest for students. (Which Bank Can do that?) She will have continued that strategy for 10 years when she finishes Uni. studies. How much will Ellen have in her account by then? Answer.36.7856 × $450 = $16,553.52
	7. What is the value after 5½ years of an annuity when, at the end of each quarter, $1,000 is deposited into an account paying 8% p.a.?
	8. At the end of each month for 2 years, Jamie contributed $300 into his superannuation account. At that time Jamie was enjoying a 12% interest rate for his account. How much will Jamie have at the end of the two years?
Find the contribution required.	9. An amount of $A is deposited into an investment account each half-year for 6 years paying 6% p.a. At the end of that period, the investment is valued at $10,644. What was the investment amount $A? Answer.$10,644 ÷ 14.1920 = $750
	10. What amount (to the nearest $10) should Virginia invest at the end of each year in an account paying 5% p.a. if she wants to have a balance of at least $22,500 by the end of 7 years? Answer.$2,770.
Equivalent single sum investments	11. Nathan invested $250 per quarter at 8% p.a. into a special fund for 9 years. (i) What values must be used to lookup the interest factor value in the Future value table? (ii) Calculate the amount in Nathan's fund at the end of the period - take the interest factor value as 51.9944. (ii) What single amount of money could Nathan have invested to develop the same amount of money in 9 years with an interest rate of 6% p.a.? Answer.(i) 36 periods and 2%. (ii) $12,998.60 (iii) Single amount of $7,605.35.
	12. At the end of 11 years of quarterly contributions to an investment fund, Andrew has $47,000 in his account. What single amount (to the nearest $10) could Andrew have deposited in account paying monthly interest at 6% p.a. over the 11 years to have saved the same amount of money?
Calculating interest	13. Alyssa makes a deposit of $500 into her superannuation account twice each year for 10 years. Her fund pays 10% p.a. (i) How much did Alyssa have invested in the fund at the end of 10 years? (ii) How much interest had Alyssa accrued over that time period in her fund? Answer.(i) Invested = $16,533 (ii) Interest = $6,533
	14. Jess made a regular monthly deposit of $150 into her special Credit Union account for 19 months. The account paid 12% p.a. interest. By the end of the 19 months: (i) what was the value of the first deposit? (ii) how much had Jess invested? (iii) how much interest had she earned in total? (iv) what was the yield on her investment? Answer.(i) Invested = $2,850 (ii) Interest = $271.64. (iii) Yield = 9.5%.
Comparing investments	15. Which of the following investment options will produce the better return: $8,000 invested annually @ 5% for 8 years. $10,000 invested annually @ 4% for 8 years. Explain why there is a difference between these two options.
	16. Which of the following investment options will produce the better return: $5,000 invested each half year @ 8% p.a. for 4 years. $3,500 invested each quarter @ 8% for 3 years. Explain the difference between these two options and suggest a reason why one option is preferable to the other.