{"id":64,"date":"2024-01-08T10:20:02","date_gmt":"2024-01-08T10:20:02","guid":{"rendered":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/3-4-effective-interest-rate\/"},"modified":"2024-09-25T08:33:23","modified_gmt":"2024-09-25T08:33:23","slug":"3-4-effective-interest-rate","status":"publish","type":"chapter","link":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/3-4-effective-interest-rate\/","title":{"raw":"3.4 Effective Interest Rate","rendered":"3.4 Effective Interest Rate"},"content":{"raw":"

Effective interest rates can be used to compare investment opportunities. The effective rate of interest is the equivalent rate of simple interest\u00a0 earned over one year for an interest rate that is compounded twice or more over the year. The annual simple interest rate will be greater than the annual compounding interest rate to earn the same amount of interest.<\/p>\r\n

The annual interest rate, r, for compounding calculations, is often called the nominal rate.<\/p>\r\n

Illustration: If RM1 is deposited at 4% compounded quarterly, the\u00a0 compound amount is RM1.0406, an increase of 4.06% over the\u00a0 original RM1. Here, the actual increase of 4.06% in the money is somewhat higher than\u00a0 the stated increase of 4%. To differentiate between these two numbers, 4% is called the nominal\u00a0 or stated rate of interest, r while 4.06% is called the effective rate, $r_{E}$ .<\/p>\r\n

The effective rate corresponding to a stated rate of interest r compounded m times per year can be calculated as follows:<\/p>\r\n

[latexpage]\r\n\\begin{equation} \\label{}\r\nr_{E} = (1 + \\frac{r}{m})^{m} - 1\r\n\\end{equation}<\/p>\r\n\r\n

Example 3.7<\/header>\r\n
\r\n

Betty needs to borrow money. Bank A charges 8% interest\u00a0 compounded semiannually. Bank B charges 7.9% interest\u00a0 compounded monthly. At which bank will she pay the lesser\u00a0 amount of interest?<\/p>\r\n[h5p id=\"16\"]\r\n\r\n<\/div>\r\n<\/div>\r\n

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

Effective interest rates can be used to compare investment opportunities. The effective rate of interest is the equivalent rate of simple interest\u00a0 earned over one year for an interest rate that is compounded twice or more over the year. The annual simple interest rate will be greater than the annual compounding interest rate to earn the same amount of interest.<\/p>\n

The annual interest rate, r, for compounding calculations, is often called the nominal rate.<\/p>\n

Illustration: If RM1 is deposited at 4% compounded quarterly, the\u00a0 compound amount is RM1.0406, an increase of 4.06% over the\u00a0 original RM1. Here, the actual increase of 4.06% in the money is somewhat higher than\u00a0 the stated increase of 4%. To differentiate between these two numbers, 4% is called the nominal\u00a0 or stated rate of interest, r while 4.06% is called the effective rate, \"r_{E}\" .<\/p>\n

The effective rate corresponding to a stated rate of interest r compounded m times per year can be calculated as follows:<\/p>\n

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

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

\n
Example 3.7<\/header>\n
\n

Betty needs to borrow money. Bank A charges 8% interest\u00a0 compounded semiannually. Bank B charges 7.9% interest\u00a0 compounded monthly. At which bank will she pay the lesser\u00a0 amount of interest?<\/p>\n

\n