Annuities

 

You invest $1000 every three months at 3.6% compounded quarterly.
(a) What will your investment be worth after 18 months.
(b) How much interest have you earned?

Calculate the rate per period

\[ \begin{align} i &= \frac{3.6}{400} \\ &= 0.009 \end{align} \ \]

Calculate the future value

The number of contributions is 6, so \[ \begin{align} V_1 &= 0 (1.009) + 1000 \\ &= 1000 \\ V_2 &= 1000(1.009) + 1000 \\ &= 2009 \\ V_3 &= 2009 (1.009) + 1000 \\ &= 3027.08 \\ V_4 &= 3027.08 (1.009) + 1000 \\ &= 4054.32 \\ V_5 &= 4054.32 (1.009) + 1000 \\ &= 5090.81 \\ V_6 &= 5090.81 (1.009) + 1000 \\ &= 6136.63 \end{align} \ \] So after 6 contributions they will have about $6136.63.

Interest Earned is future value less total contributions

\[ \begin{align} \text{Future value } &= 6136.63 \\ \text{Total contributions } &= 6000 \\ \text{Interest Earned } &= 136.63 \\ \end{align} \ \]

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 $3000 every six months at 4.6% compounded half-yearly.
(a) What will your investment be worth after 24 months.
(b) How much interest have you earned?