{"id":100,"date":"2024-01-09T07:39:32","date_gmt":"2024-01-09T07:39:32","guid":{"rendered":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/5-4-annuity-due\/"},"modified":"2024-09-25T08:37:18","modified_gmt":"2024-09-25T08:37:18","slug":"5-4-annuity-due","status":"publish","type":"chapter","link":"https:\/\/openbook.ums.edu.my\/financialmathematicsineconomics\/chapter\/5-4-annuity-due\/","title":{"raw":"5.4 Annuity due","rendered":"5.4 Annuity due"},"content":{"raw":"

Annuity due is an annuity whose periodic payments are paid at the beginning of each payment period. The term of an annuity due starts at the time of the first payment and ends one payment period after the date of the last payment. This can be illustrated as figure below.<\/p>\r\n\r\n\r\n[caption id=\"attachment_99\" align=\"aligncenter\" width=\"300\"]\"\" Figure 2: Illustration of an annuity due timeline[\/caption]\r\n

Annuity due also known as annuities payable in advance and normally arise in respect of insurance premiums, rents, etc.<\/p>\r\n

[latexpage]<\/p>\r\n

We know that the future value of the payments at the end of the (n \u2212 <\/em>1)th period is R$s_{\\bar{n}\\mid{i}}$<\/em>. We then accumulate it\u00a0<\/em>for 1 interest period, to obtain the future value of an annuity due, $s_{\\ddot{n}\\mid{i}}$ at the end of the term as;<\/p>\r\n

Future value, $s_{\\ddot{n}\\mid{i}} = Rs_{\\bar{n}\\mid{i}}(1+i)$<\/p>\r\n

While the present value of the payments one period before the first payment is R$a_{\\bar{n}\\mid{i}}$<\/em> . To obtain the present value of an annuity due, R$a_{\\ddot{n}\\mid{i}}$<\/em> (i.e. on the date of the first payment), we accumulate R$a_{\\bar{n}\\mid{i}}$<\/em>\u00a0<\/em>for one interest period so that:<\/p>\r\n

Present value, $a_{\\ddot{n}\\mid{i}}$ <\/em>= R $a_{\\bar{n}\\mid{i}} (1+i)$<\/em><\/p>\r\n\r\n

Example 5.5<\/header>\r\n
\r\n

Mrs. Mary deposits RM100 at the beginning of each year for 10 years in an account paying 12% p.a. How much is in her account at the end of 10 years?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

Example 5.6<\/header>\r\n
\r\n

The monthly rent for a flat is RM520 payable at the beginning of each month. If money is worth i<\/em>12<\/sub> = 9%, what is the equivalent yearly rental payable in advance?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

Example 5.7<\/header>\r\n
\r\n

A man saves RM15000 at the beginning of each year to accumulate a fund expansion. If the fund earns 15% p.a., what is the amount he will have at the end of 5 years?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n[h5p id=\"27\"]","rendered":"

Annuity due is an annuity whose periodic payments are paid at the beginning of each payment period. The term of an annuity due starts at the time of the first payment and ends one payment period after the date of the last payment. This can be illustrated as figure below.<\/p>\n

\"\"
Figure 2: Illustration of an annuity due timeline<\/figcaption><\/figure>\n

Annuity due also known as annuities payable in advance and normally arise in respect of insurance premiums, rents, etc.<\/p>\n

\n

We know that the future value of the payments at the end of the (n \u2212 <\/em>1)th period is R\"s_{\bar{n}\mid{i}}\"<\/em>. We then accumulate it\u00a0<\/em>for 1 interest period, to obtain the future value of an annuity due, \"s_{\ddot{n}\mid{i}}\" at the end of the term as;<\/p>\n

Future value, \"s_{\ddot{n}\mid{i}} = Rs_{\bar{n}\mid{i}}(1+i)\"<\/p>\n

While the present value of the payments one period before the first payment is R\"a_{\bar{n}\mid{i}}\"<\/em> . To obtain the present value of an annuity due, R\"a_{\ddot{n}\mid{i}}\"<\/em> (i.e. on the date of the first payment), we accumulate R\"a_{\bar{n}\mid{i}}\"<\/em>\u00a0<\/em>for one interest period so that:<\/p>\n

Present value, \"a_{\ddot{n}\mid{i}}\" <\/em>= R \"a_{\bar{n}\mid{i}} (1+i)\"<\/em><\/p>\n

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Example 5.5<\/header>\n
\n

Mrs. Mary deposits RM100 at the beginning of each year for 10 years in an account paying 12% p.a. How much is in her account at the end of 10 years?<\/p>\n<\/div>\n<\/div>\n

\n
Example 5.6<\/header>\n
\n

The monthly rent for a flat is RM520 payable at the beginning of each month. If money is worth i<\/em>12<\/sub> = 9%, what is the equivalent yearly rental payable in advance?<\/p>\n<\/div>\n<\/div>\n

\n
Example 5.7<\/header>\n
\n

A man saves RM15000 at the beginning of each year to accumulate a fund expansion. If the fund earns 15% p.a., what is the amount he will have at the end of 5 years?<\/p>\n<\/div>\n<\/div>\n

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