Annuities

 

Alice and Bob invest $2000 every six months at 7.5% 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 $80000?

Calculate the rate per period and number of periods

\[ \begin{align} \text{r} &= \frac{7.5}{200} \\ &= 0.0375 \\ \text{nper} &= 10 \times 2 \\ &= 20 \end{align} \ \]

Calculate the future value

Using a spreadsheet Future Value function: \[ \begin{align} \text{Future Value } &= FV(0.0375, 20, -2000) \\ &= 58,034.77 \\ \end{align} \ \]

Use the spreadsheet PMT function to calculate the required payments

\[ \begin{align} \text{Payment }&= PMT(0.0375, 20, 0, -80000) \\ &= 2756.97 \end{align} \ \]

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:

Alice and Bob invest $2000 every three months at 8% compounded quarterly.
(a) Use a spreadsheet function to find the value of the investment after 8 years.
(b) What contribution would be required for a future value of $90000?