Financial Arithmetic - SS3 Mathematics Past Questions and Answers - page 1

\[A = P(1 + R)^{T}\]

\[P = 12000\ \ \ R = 20\% = 0.2\ \ \ \ \ T = 5\]

\[A = 12000{(1 + 0.2)}^{5}\]

\[A = 12000{(1.2)}^{5}\]

\(A = N29,859.84\ \cong N29,860\ \ \)

\[15\%\ dividend\ on\ the\ face\ value\ of\ shares\ held\ = \ 10\%\ of\ (1,000 \times 50k)\]

\[= 15\%\ of\ 50,000k\]

= 7,500k

= N75

\[Bond\ interest\ (coupon) = \ 2500000 \times 0.08 \times 10 = N2,000,000\]

\(Maturity\ value = N2,500,000 + N2,000,000 = N4,500,000\)

\[A = P\left( 1 + \frac{R}{n} \right)^{nT}\]

\[P = 15000\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R = 10\% = 0.1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 4\ \ \ \ \ \ \ \ \ \ \ \ \ T = 15\]

\[A = 15000\left( 1 + \frac{0.1}{4} \right)^{4(15)}\]

\[A = 15000(1 + 0.025)^{60}\]

\[A = 15000(1.025)^{60}\]

\[A = N65,996.85\]

\[S = 5000000,\ i = \frac{0.15}{12} = 0.0125,\ n = 5 \times 12 = 60\]

\[R = \frac{5000000 \times 0.0125}{(1 + 0.0125)^{60} - 1}\]

\[R = \frac{5000000(0.0125)}{1.10718} = 56,449.72\]

\[R = N56,449.72\]

\[P = 250000\ ,\ i = \frac{0.1}{12} = 0.0083333,\ n = 30 \times 12 = 360\]

\[R = \frac{250000(0.0083333)}{1 - \left( \frac{1}{1 + 0.0083333} \right)^{360}} = \$ 2,193.92\]

\[Therefore,\ book\ value\ after\ 3\ years\ = \ N4,605,937.50\]