Annuities

 

Alice and Bob invest $5000 every six months at 5.5% compounded half-yearly.
(a) What will their investment be worth after 3 years.
(b) How much interest have they earned?

Calculate the rate per period

\[ \begin{align} i &= \frac{5.5}{200} \\ &= 0.0275 \end{align} \ \]

Calculate the future value

The number of contributions is 6, so \[ \begin{align} V_1 &= 0 (1.0275) + 5000 \\ &= 5000 \\ V_2 &= 5000(1.0275) + 5000 \\ &= 10137.50 \\ V_3 &= 10137.50 (1.0275) + 5000 \\ &= 15416.28 \\ V_4 &= 15416.28 (1.0275) + 5000 \\ &= 20840.23 \\ V_5 &= 20840.23 (1.0275) + 5000 \\ &= 26413.34 \\ V_6 &= 26413.34 (1.0275) + 5000 \\ &= 32139.70 \end{align} \ \] So after 6 contributions they will have about $32139.70.

Interest Earned is future value less total contributions

\[ \begin{align} \text{Future value } &= 32139.70 \\ \text{Total contributions } &= 30000 \\ \text{Interest Earned } &= 2139.70 \\ \end{align} \ \]

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 $3000 every six months at 5.2% compounded half-yearly.
(a) What will their investment be worth after 4 years.
(b) How much interest have they earned?