WACE Maths Applications cheat sheet

Mathematics Applications

• Simple interest: I = P × r × t, where r is the annual rate as a decimal and t is time in years; total amount A = P(1 + rt).

• Compound interest: A = P(1 + r)^n, where n is the number of compounding periods; solve for P, r, or n by rearranging or using logarithms.

• Reducing-balance loans: the recurrence is B(n+1) = B(n)(1 + r) − R, where R is the repayment per period; iterate or use a spreadsheet to track the balance.

• Straight-line depreciation: value V = V0 − D × t; declining-balance depreciation: V = V0(1 − r)^t, matching compound-interest structure.

• Inflation and appreciation use the same compound formula with a positive rate; purchasing power falls as prices rise, so real value = nominal value ÷ (1 + r)^t.

• Effective annual rate from nominal rate r compounded m times per year: EAR = (1 + r/m)^m − 1; compare rates only via effective rates.

• Doubling time under compound growth is approximately 70 ÷ (percentage growth rate per period), valid for small rates.

• Sequences: arithmetic Tn = a + (n − 1)d with sum Sn = n/2(2a + (n − 1)d); geometric Tn = a·r^(n−1) with sum Sn = a(r^n − 1)/(r − 1).