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This document discusses the time value of money and how interest rates affect present and future values of investments. It provides examples of how to calculate the future value of a single amount invested at a given interest rate over time, as well as the doubling period of investments. The document also demonstrates how to calculate the present and future values of annuities using discount and compounding factors.
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Bonds are fixed income securities that promise regular interest payments and repayment of principal at maturity. There are various types including treasury bonds, corporate bonds, and treasury bills. Key bond characteristics include par value, coupon payments, coupon rate, maturity date, and whether it is a floating or zero coupon bond. The bond indenture contract specifies payment terms, collateral, covenants, and other details. Bond valuation considers factors like coupon payments, yield, number of periods, and maturity value. Bond prices are affected by yield to maturity, time to maturity, and coupon size.
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Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are "discounted" at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations.[2]
Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3]
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Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.
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Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
FV = PV x (1 + (i / n)) ^ (n x t)
For example, assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:
PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673
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Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
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i = interest rate
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FV = PV x (1 + (i / n)) ^ (n x t)
For example, assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:
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4. la metafisica moderna y la teoria de la complejidad
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【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：A575476】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：A575476】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
一比一原版(RMIT毕业证)皇家墨尔本理工大学毕业证如何办理
RMIT硕士学位证成绩单【微信95270640】《皇家墨尔本理工大学毕业证书》《QQ微信95270640》学位证书电子版：在线制作皇家墨尔本理工大学毕业证成绩单GPA修改（制作RMIT毕业证成绩单RMIT文凭证书样本）、皇家墨尔本理工大学毕业证书与成绩单样本图片、《RMIT学历证书学位证书》、皇家墨尔本理工大学毕业证案例毕业证书制作軟體、在线制作加拿大硕士学历证书真实可查.
【本科硕士】皇家墨尔本理工大学皇家墨尔本理工大学本科学位证成绩单（GPA修改）；学历认证（教育部认证）；大学Offer录取通知书留信认证使馆认证；雅思语言证书等高仿类证书。
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1客户提供办理皇家墨尔本理工大学皇家墨尔本理工大学本科学位证成绩单信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
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真实网上可查的证明材料
1教育部学历学位认证留服官网真实存档可查永久存档。
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我们对海外大学及学院的毕业证成绩单所使用的材料尺寸大小防伪结构（包括：皇家墨尔本理工大学皇家墨尔本理工大学本科学位证成绩单隐形水印阴影底纹钢印LOGO烫金烫银LOGO烫金烫银复合重叠。文字图案浮雕激光镭射紫外荧光温感复印防伪）都有原版本文凭对照。质量得到了广大海外客户群体的认可同时和海外学校留学中介做到与时俱进及时掌握各大院校的（毕业证成绩单资格证结业证录取通知书在读证明等相关材料）的版本更新信息能够在第一时间掌握最新的海外学历文凭的样版尺寸大小纸张材质防伪技术等等并在第一时间收集到原版实物以求达到客户的需求。
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