Problem 56165. Ordinary Annuity : Number of Payments (Present Value)

Created by Mehmet OZC

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 230.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.367px; transform-origin: 407px 115.367px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.5px 8px; transform-origin: 151.5px 8px; unicode-bidi: normal; "><span style="">Theorem : Present Value of an Ordinary Annuity</span></span></div><div style="block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-16px"><img src="data:image/png;base64,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" style="width: 116px; height: 38px;" width="116" height="38"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; "><span style="">where;</span></span></div><ul style="block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; "><span style="">P : Present value of all payments</span></span></li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; "><span style="">A : Periodic payment</span></span></li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; "><span style="">r : Interest rate per period</span></span></li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; "><span style="">n : Number of periods (peyments)</span></span></li></ul><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; "><span style="">Calculate n, given P, A and r. </span></span></div></div></div>

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Problem 56165. Ordinary Annuity : Number of Payments (Present Value)

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Problem 56165. Ordinary Annuity : Number of Payments (Present Value)

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