{"id":62,"date":"2023-12-31T02:55:00","date_gmt":"2023-12-31T02:55:00","guid":{"rendered":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/effective-interest-rate\/"},"modified":"2024-09-25T08:33:00","modified_gmt":"2024-09-25T08:33:00","slug":"effective-interest-rate","status":"publish","type":"chapter","link":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/effective-interest-rate\/","title":{"raw":"3.3 Compound Discount","rendered":"3.3 Compound Discount"},"content":{"raw":"

3.3.1 Compound Discount at a Discount Rate<\/h1>\r\n

Let dm<\/sup> be the nominal rate of discount compounded m times per year.<\/p>\r\n

Then the discount rate per conversion period is dm<\/sup>\/m and the discounted value \ud835\udc43 of a future amount \ud835\udc46 due in \ud835\udc5b periods is<\/p>\r\n

[latexpage]\r\n\\begin{equation} \\label{eq:1}\r\nP = S(1 - \\frac{{d}^{m}}{m})^{n}\r\n\\end{equation}<\/p>\r\n

Thus, the accumulated value $S$ is:<\/p>\r\n

[latexpage]\r\n\\begin{equation} \\label{eq:2}\r\nS = P(1 - \\frac{{d}^{m}}{m})^{-n}\r\n\\end{equation}<\/p>\r\n\r\n

Example 3.5<\/header>\r\n
\r\n

Find the discounted value of RM1000 due in 2 years at d =12% compounded monthly.<\/p>\r\n[h5p id=\"14\"]\r\n\r\n<\/div>\r\n<\/div>\r\n

Example 3.6<\/header>\r\n
\r\n

Find the discounted value of RM1000 due in 2 years at d=7% compounded daily.<\/p>\r\n

[h5p id=\"15\"]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

<\/p>","rendered":"

3.3.1 Compound Discount at a Discount Rate<\/h1>\n

Let dm<\/sup> be the nominal rate of discount compounded m times per year.<\/p>\n

Then the discount rate per conversion period is dm<\/sup>\/m and the discounted value \ud835\udc43 of a future amount \ud835\udc46 due in \ud835\udc5b periods is<\/p>\n

\n<\/a><\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

Thus, the accumulated value \"S\" is:<\/p>\n

\n<\/a><\/p>\n

(2) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

\n
Example 3.5<\/header>\n
\n

Find the discounted value of RM1000 due in 2 years at d =12% compounded monthly.<\/p>\n

\n