{"id":48,"date":"2023-11-02T06:18:43","date_gmt":"2023-11-02T06:18:43","guid":{"rendered":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/2-4-simple-discount\/"},"modified":"2024-09-25T08:32:16","modified_gmt":"2024-09-25T08:32:16","slug":"2-4-simple-discount","status":"publish","type":"chapter","link":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/2-4-simple-discount\/","title":{"raw":"2.4 Simple Discount","rendered":"2.4 Simple Discount"},"content":{"raw":"

2.4.1 Simple Discount at an Interest Rate<\/strong><\/h1>\r\n[latexpage]\r\n

In discounting at simple interest, the difference $D = S \u2013 P$ is called the simple discount (on $S$) at an interest rate ($r$). We may interpret $D$ either as the interest $I$ on $P$ which when added to $P$ gives $S$, or as the true discount on $S$ which when substracted from $S$ gives $P$.<\/p>\r\n\r\n

2.4.2 Simple Discount at a Discount Rate<\/strong><\/h1>\r\n

The discount rate $d$ for a year is the ratio of the discount $D$ for the year to the amount $S$ on which the discount is given. The simple discount $D$ on an amount $S$, also called bank discount, for $t$ years at the discount rate $d$, which can be calculated as follows:<\/p>\r\n\\begin{equation} \\label{eq:5}\r\n\r\nD = S \\times d \\times t\r\n\r\n\\end{equation}\r\n\r\nAnd the discounted value, or proceeds, $P$ of $S$ is given by\r\n\r\n[latexpage]\r\n\\begin{equation} \\label{eq:6}\r\nP = S - D = S - Sdt = S(1 - dt)\r\n\\end{equation}\r\n

The charge for some short-term loans may be based on the final amount rather than on the present value. The lender calculates the bank discount $D$ on the final amount $S$ that must be paid on the due date and deducts it from $S$; the borrower receives the proceeds $P$. For this reason, bank discount is sometimes called interest in advance. The following equation calculate the maturity value of a loan for specified proceeds\/ principals\/ present values of $S$.<\/p>\r\n[latexpage]\r\n\r\n\\begin{equation} \\label{eq:7}\r\n\r\nS = \\frac{P}{1-dt} = P(1-dt)^{-1}\r\n\r\n\\end{equation}\r\n

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Example 2.4<\/p>\r\n\r\n<\/header>\r\n

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Find the present value of 12% simple discount of $1000 due in 5 months. What is the simple discount?<\/p>\r\n[h5p id=\"7\"]\r\n\r\n<\/div>\r\n<\/div>\r\n

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Example 2.5<\/p>\r\n\r\n<\/header>\r\n

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Calculate the present value of RM1000 due in 1 year at a simple discount rate of 10% p.a.<\/p>\r\n[h5p id=\"8\"]\r\n\r\n<\/div>\r\n<\/div>\r\n ","rendered":"

2.4.1 Simple Discount at an Interest Rate<\/strong><\/h1>\n

In discounting at simple interest, the difference \"D = S - P\" is called the simple discount (on \"S\") at an interest rate (\"r\"). We may interpret \"D\" either as the interest \"I\" on \"P\" which when added to \"P\" gives \"S\", or as the true discount on \"S\" which when substracted from \"S\" gives \"P\".<\/p>\n

2.4.2 Simple Discount at a Discount Rate<\/strong><\/h1>\n

The discount rate \"d\" for a year is the ratio of the discount \"D\" for the year to the amount \"S\" on which the discount is given. The simple discount \"D\" on an amount \"S\", also called bank discount, for \"t\" years at the discount rate \"d\", which can be calculated as follows:<\/p>\n

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

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

And the discounted value, or proceeds, \"P\" of \"S\" is given by<\/p>\n

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

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

The charge for some short-term loans may be based on the final amount rather than on the present value. The lender calculates the bank discount \"D\" on the final amount \"S\" that must be paid on the due date and deducts it from \"S\"; the borrower receives the proceeds \"P\". For this reason, bank discount is sometimes called interest in advance. The following equation calculate the maturity value of a loan for specified proceeds\/ principals\/ present values of \"S\".<\/p>\n

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

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

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Example 2.4<\/p>\n<\/header>\n

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Find the present value of 12% simple discount of $1000 due in 5 months. What is the simple discount?<\/p>\n

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