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These are the solutions to Cambridge Ordinary Level (O-Level) past questions on the Mathematics of Finance.
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(1.) Monthly interest payment = Monthly interest rate * Average balance
(2.) Net monthly cash flow = Monthly income − Monthly expenses
$ (1.)\:\: SI = Prt \\[3ex] (2.)\:\: SI = A - P \\[3ex] (3.)\:\: P = \dfrac{SI}{rt} \\[5ex] (4.)\:\: t = \dfrac{SI}{Pr} \\[5ex] (5.)\:\: r = \dfrac{SI}{Pt} \\[5ex] (6.)\:\: A = P + SI \\[3ex] (7.)\:\: A = P(1 + rt) \\[3ex] (8.)\:\: P = \dfrac{A}{1 + rt} \\[5ex] (9.)\:\: t = \dfrac{A - P}{Pr} \\[5ex] (10.)\:\: r = \dfrac{A - P}{Pt} \\[5ex] (11.)\:\: SI = \dfrac{Art}{1 + rt} $
$
(1.)\:\: A = P\left(1 + \dfrac{r}{m}\right)^{mt} \\[7ex]
(2.)\:\: P = \dfrac{A}{\left(1 + \dfrac{r}{m}\right)^{mt}} \\[10ex]
(3.)\:\: r = m\left[\left(\dfrac{A}{P}\right)^{\dfrac{1}{mt}} - 1\right] \\[10ex]
(4.)\:\: r = m\left(10^{\dfrac{\log\left(\dfrac{A}{P}\right)}{mt}} - 1\right) \\[10ex]
(5.)\:\: t = \dfrac{\log\left(\dfrac{A}{P}\right)}{m\log\left(1 + \dfrac{r}{m}\right)} \\[7ex]
(6.)\:\: A = P + CI \\[3ex]
(7.)\:\: CI = A - P \\[3ex]
(8.)\:\: A = P(1 + i)^n \\[4ex]
(9.)\:\: P = \dfrac{A}{(1 + i)^n} \\[7ex]
(10.)\:\: i = \dfrac{r}{m} \\[5ex]
(11.)\:\: n = mt \\[3ex]
(12.)\;\; Total\;\;Return = \dfrac{A - P}{P} * 100\% \\[7ex]
(13.)\;\; Annual\;\;Return = \left[\left(\dfrac{A}{P}\right)^{\dfrac{1}{t}} - 1\right] * 100\% \\[7ex]
$
Future Value (Amount) of Cash Flows (Principal) for Several Years
$
(13.)\:\:At\:\:the\:\:end\:\:of\:\:each\:\:year:\:\: FV = PV\left(1 +
\dfrac{r}{m}\right)^{m(last\:\:year - that\:\:year)} \\[7ex]
(14.)\:\: Total\:FV = \Sigma FV
$
Values of $m$
| If Compounded: | m = |
|---|---|
| Annually |
$1$ ($1$ time per year) Also means every twelve months |
| Semiannually |
2 (2 times per year) Also means every six months |
| Quarterly |
4 (4 times per year) Also means every three months |
| Monthly |
12 (12 times per year) Also means every month |
| Weekly | 52 (52 times per year) |
| Daily (Ordinary/Banker's Rule) | 360 (360 times per year) |
| Daily (Exact) | 365 (365 times per year) |