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...

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.

Asked on by saj-94

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llltkl | College Teacher | (Level 3) Valedictorian

Posted on

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` .

Sources:

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