Financial Mathematics

**Financial Mathematics**

**Present Value:**Present value describes how much a future sum of money is worth today. It accounts for the fact that money we receive today can be invested to earn a return.

If money is wroth

*i*per period, then present value

*P*of amount

*S*due

*n*periods hence is given by

*P = S*(1 +

*i*)

^{−n}

**Amount of an Annuity:**The future value of an annuity is the value of a group of recurring payments at a certain date in the future, assuming a particular rate of return, or discount rate.

The future value

*S*of an ordinary annuity of ₹

*R*per period for

*n*periods at the rate

*i*per period is given by

$S=R\left\{\frac{{\left(1+i\right)}^{n}-1}{i}\right\}$

**Present Value of an Annuity:**The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate.

The present value

*P*of an ordinary annuity of ₹

*R*per payment period for

*n*periods at the rate

*i*per period is given by

$P=R\left\{\frac{1-{\left(1+i\right)}^{-n}}{i}\right\}$

**Amount in a Sinking Fund**

The amount in a sinking fund at any time is the amount of the annuity formed by the payments. Thus, the amount S in a sinking fund at any time is given by

$S=R\left\{\frac{{\left(1+i\right)}^{n}-1}{i}\right\}\phantom{\rule{0ex}{0ex}}R=\mathrm{Periodic}\mathrm{deposit}\mathrm{or}\mathrm{payment}\phantom{\rule{0ex}{0ex}}n=\mathrm{Number}\mathrm{of}\mathrm{periodic}\mathrm{deposits}\phantom{\rule{0ex}{0ex}}i=\mathrm{Interest}\mathrm{per}\mathrm{period}$

**Sinking Fund Payment**

The periodic payment of ₹ R is required to accumulate a sum of ₹ S over n periods with interest…

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