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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

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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