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# 金融代写|企业融资代写Corporate Finance代考|FINC2011 Annuity

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## 金融代写|企业融资代写Corporate Finance代考|Annuity

An annuity is a level stream of regular payments that lasts for a fixed number of periods. Not surprisingly, annuities are among the most common kinds of financial instruments. The pensions that people receive when they retire are often in the form of an annuity. Leases and mortgages are also often annuities.

To figure out the present value of an annuity we need to evaluate the following equation:
$$\frac{C}{1+r}+\frac{C}{(1+r)^2}+\frac{C}{(1+r)^3}+\ldots+\frac{C}{(1+r)^T}$$
The present value of only receiving the coupons for $T$ periods must be less than the present value of a consol, but how much less? To answer this we have to look at consols a bit more closely.

## 金融代写|企业融资代写Corporate Finance代考|Growing Annuity

Cash flows in business are very likely to grow over time, due either to real growth or to inflation. The growing perpetuity, which assumes an infinite number of cash flows, provides one formula to handle this growth. We now consider a growing annuity, which is a finite number of growing cash flows. Because perpetuities of any kind are rare, a formula for a growing annuity would be useful indeed. The formula is ${ }^{13}$
Formula for Present Value of Growing Annuity:
$$\mathrm{PV}=C\left[\frac{1}{r-g}-\frac{1}{r-g} \times\left(\frac{1+g}{1+r}\right)^T\right]$$
where, as before, $C$ is the payment to occur at the end of the first period, $r$ is the interest rate, $g$ is the rate of growth per period, expressed as a percentage, and $T$ is the number of periods for the annuity.

## 金融代写|企业融资代写CORPORATE FINANCE代 考|ANNUITY

$$\frac{C}{1+r}+\frac{C}{(1+r)^2}+\frac{C}{(1+r)^3}+\cdots+\frac{C}{(1+r)^T}$$

## 金融代写|企业融资代写CORPORATE FINANCE代 考|GROWING ANNUITY

$$\mathrm{PV}=C\left[\frac{1}{r-g}-\frac{1}{r-g} \times\left(\frac{1+g}{1+r}\right)^T\right]$$

## Matlab代写

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