A woman wishes to retire when she is 60 years old. She has 35 years to build up her savings and would like to have R1 000 000 saved as a lump sum by the time she retires. She decides to invest in an ordinary annuity, with interest given at 6.5% per annum, compounded monthly.

a) Determine the amount of the monthly contribution which she will require to make to achieve her goal if she contributes monthly for 35 years.

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The future value of an annuity is given by:

`S=R(((1+i)^n -1)/i)`

(where, R is the monthly contribution amount; i, the rate of interest and n is the number of periods).

Here, the payments and interest compounding occur monthly, so the interest rate per period is 0.065/12=0.005416667

and the number of compounding periods is 35*12 = 420.

Substituting the information into the formula for future value of an annuity gives:

`1000000=R(((1+0.005416667)^420-1)/0.005416667)`

`rArr R=(1000000*0.005416667)/((1.005416667)^420-1)`

`=624.9`

`~~ 625`

Thus, the required monthly contribution is `R 625` .

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