Annuities

 

You take out a reducing balance loan of $10000 at a rate of 4% compounded quarterly for 3 years and agree to repay $888.49 every quarter.
(a) What will be the balance after 12 months.
(b) How much interest have you paid so far?

Calculate the rate per period

\[ \begin{align} i &= \frac{4.0}{400} \\ &= 0.01 \end{align} \ \]

Calculate the balance outstanding after 12 months

The number of repayments after 12 months is 4, so \[ \begin{align} V_1 &= 10000(1.01) - 888.49 \\ &= 9211.51 \\ V_2 &= 9211.51(1.01) - 888.49 \\ &= 8415.14 \\ V_3 &= 8415.14(1.01) - 888.49 \\ &= 7610.80 \\ V_4 &= 7610.80(1.01) - 888.49 \\ &= 6798.41 \\ \end{align} \ \] So after 4 repayments the balance outstanding is 6798.41.

Interest Paid is Repayments + Balance Outstanding - Loan Amount

\[ \begin{align} \text{Present value } &= 6798.41 \\ \text{Repayments } &= 888.49 \times 4 = 3553.96 \\ \text{Interest Paid } &= 3553.96 + 6798.41 - 10000 \\ &= 352.37 \end{align} \ \]

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 take out a reducing balance loan of $15000 at a rate of 6% compounded half-yearly for 3 years and agree to repay $2769 every six months.
(a) What will be the balance after 18 months.
(b) How much interest have you paid so far?