Question

1. Calculate the annuity factor and amount needed to be invested for 7 years’ income at $33,000 p.a. starting in three years with rates at 3.4%.

2. What is the future value of saving $1,000 each year for the next 20 years if you can deposit at 2.3%?

3. You wish to set up a regular savings plan for your retirement in 27 years’ time. Interest rates are currently 2.5% with long term inflation at 0.5%.You believe that interest rates will be at 4% in 2047. You wish to have an annual income of $52,000 for 20 years from the pension in today’s money growing at 1% a year. How much do you need to invest each year?

4. You will save $12,000.00 this year and increase this by 1.0% each year for the next 17 years. How much will you have at the end of the saving period if interest rates are 3.5%?

5. What annuity would this (answer to question 4) give you in 18 years if interest rates are then % and the income should last for 12 years?  What would the effect on the initial payment be if the annual pension was required to grow by 1% p.a.?

6. You take out a loan to buy a new car for an amount of CHF 70,000 at an interest rate of 4% p.a. If you want to repay capital and interest in equal monthly installments, how much should you pay a month to repay the loan in four years?

7. What is your constant quarterly repayment amount to repay capital and interest on a mortgage of USD 450,000 over 25 years at 3.5% p.a.?

8. How much do you need to repay each year to repay a loan of $300,000 over 20 years at 7% in regular payments? How much should you pay on a monthly basis to fulfill the same repayment period?

9. If you save £650 a month how much do you have in 12 years’ time if you can deposit at a constant rate of 4.3% p.a.?

10. What pension would the amount in question 9 give you paid on a quarterly basis if rates are then 5% and the pension should last for 8 years?

Answer 1

Let A be the amount which needs to be deposited to get $33000 p.a. for 7 years Starting at the end of 3 years

then A should equal the present value of the future income

A= 33000/1.034^3+33000/1.034^4+......+33000/1.034^9

=1/1.034^2* (33000/1.034+33000/1.034^2+......+33000/1.034^7)

= 1/1.034^2* 33000/0.034*(1-1/1.034^7)

= $189434.59 which is the required amount to be deposited

Annuity Factor = 189434.59/33000 = 5.74044

or Annuity factor = 1/1.034^2*(1/1.034+1/1.034^2+....+1/1.034^7)

=1/1.034^2*1/0.034*(1-1/1.034^7)

=5.74044