Annuities

 

You invest $1000 every six months at 4.8% compounded half-yearly.
(a) Use a spreadsheet function to find the value of the investment after 10 years.
(b) What contribution would be required for a future value of $30000?

Calculate the rate per period and number of periods

\[ \begin{align} \text{r} &= \frac{4.8}{200} \\ &= 0.024 \\ \text{nper} &= 10 \times 2 \\ &= 20 \end{align} \ \]

Calculate the future value

Using a spreadsheet Future Value function: \[ \begin{align} \text{Future Value } &= FV(0.024, 20, -1000) \\ &= 25289.09 \\ \end{align} \ \]

Use the spreadsheet PMT function to calculate the required payments

\[ \begin{align} \text{Payment }&= PMT(0.024, 20, 0, -30000) \\ &= 1186.28 \end{align} \ \]

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

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Now You Try:

You invest $1000 every three months at 2.1% compounded quarterly.
(a) Use a spreadsheet function to find the value of the investment after 11 years.
(b) What contribution would be required for a future value of $33000?