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Financial Maths - Annuities and Future value tables.
Test Yourself 2.


 

Answer the following questions using the table elsewhere when required:

Find the future value of an annuity. 1. Ishbel wishes to invest $300 per quarter into a special savings plan. The account pays 8% p.a. compounding quarterly.

How much will she have in her account at the end of 12 months?

Answer.$300 × 4.1216 = $1,236.48.
  2. What is the future value of an annuity paying compound interest at the rate of 4% p.a. if $800 is invested each six months for 4 years?
Answer.$800 × 8.5830 = $6,866.40.
  3. Eva has her own superannuation annuity account. It pays 12% p.a. interest which is compounded monthly.

She makes payments of $200 at the end of each month and plans to continue making these deposits for 2 years.

(i) How much will Eva have in her account at the end of the 2 years?

(ii) How much will Eva have contributed across the whole period?

(iii) How much interest has Eva accumulated?

Answer.(i) Total in account = $5,394.70.
(ii) Contributions = $4,800.
(iii) Interest = $595.70.
  4. What sum of money should be invested today to produce the same result as investing $1,000 every quarter for 10 years at an interest rate of 6% p.a. compounded quarterly.
  5. Stephan contributes $2,000 to an investment account paying 6% p.a. at the end of each half year. After 4 years, the interest rate increases to 8% p.a. and Stephan contributes only for one more year.

(i) How much is in Stephan's account at the end of the 4th year immediately after he makes his 8th payment?

(ii) How much is in Stephan's account at the end of the 5th year?

Answer.(i) After 4 years: $17,784.60
(ii) Final amount is $21,235.82.
  6. Aunty Daisy opens an annuity investment account and makes a $1200 deposit at the end of each year for 8 years. Interest compounds annually.

For the first 6 years, the interest rate is 4% p.a. but for the final 2 years, the interest rate decreases to 3% p.a.

Using the table included elsewhere, determine the total amount in Aunty Daisy's account at the end of the 8 years immediately after her last payment.

 
Find the contribution required. 7. Ted is planning an overseas trip in 3 years. He wishes to save up $25,000 for his trip by investing in an annuity. He has chosen an account that pays 4% p.a., compounded quarterly.

Use the table of future values for an annuity of $1 shown above, find the amount (to the nearest $10) that Ted needs to invest each quarter to achieve his goal.

Answer.$1,970.
  8. The owners in a Strata Title block of home units estimate repair and painting the block in 5 years will require $60,000.

Their Special Maintenance Fund pays 8% p.a. payable quarterly.

What is the total amount of Strata levies they will have to collect each quarter from now to meet their target (to the nearest $1)?

Answer.$2,048 per quarter.
 

9. The table below shows the interest factors for an investment of $1 at varying interest rate for n years.

 

(i) Kamala opens an annuity account paying 6% p.a. and she makes contributions of $2,500 at the end of each year for 5 years.

Calculate the total value of Kamala's annuity after she makes her 5th contribution.

(ii) If Kamala had wanted to have $20,000 in her annuity account, what yearly contributions (to the nearest $10) would she have to make?

Answer.(i) 5,6372 × 2500 = $14,092.75.
(ii) 20,000 ÷ 5.6371 = $3.550.
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