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## How do you work out a reducing balance loan question in further maths?

1A loan of $12 000 is to be repaid in instalments of$2700 per year with an interest rate of
16% per annum being charged on the unpaid balance at the end of each year. After four
repayments, calculate:
a the amount still owing
b the interest charged to date

Set up a table with headings:
(i) Starting balance
(ii) Interest charged = (i) * interest rate
(iii) Amount paid
(iv) Ending balance = (i) + (ii) - (iii)

Year 1:
(i) $12,000 (ii)$12,000 * 0.16 = $1,920 (iii)$2,700
(iv) $12,000 +$1,920 - $2,700 =$11,220

Year 2:
(i) $11,220 (ii)$1,795.2
(iii) $2,700 (iv)$10,315.2

Year 3:
(i) $10,315.2 (ii)$1,650.43 (rounded)
(iii) $2,700 (iv)$9,265.63 (rounded)

Year 4:
(i) $9,265.63 (ii)$1,482.50
(iii) $2,700 (iv)$8,048.13

Answer to a) $8,048.13 Answer to b)$1,920 + $1,795.2 +$1650.43 + $1482.50 =$6,848.13
(or you can do a simple calculation: $2,700 * 4 is how much you paid =$10,800, but your balance only reduced by $12,000 -$8,048.13 = $3,951.87 -- therefore you paid$10,800 - $3,951.87 =$6,848.13 in interest - this is also a good way to sense-check your answer!)

Excellent answer. Use MathJax and LaTeX for nicer formatting next time. http://www.mathjax.org/demos/tex-samples/
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