Annuity - Present Value and Future Value

Annuity – Present Value and Future Value

[Watch Video for Detailed Explanation]

An annuity is a stream of regular periodic payment made or received for a specific period of time.

In annuities payments can be made at the end of period or at the beginning of the period. If payments are made at the end of the period, they are called ordinary annuity and if the payments are made at the beginning of the period, they are called annuity due. If payments are identical or equal for the period, they are called level annuities. In this section we are going to study ordinary level annuities.

1. Future Value of an Annuity

Formula for future (compound) value of an annuity is:

$FVAn=R\left(1+i\right)^{n-1}+R\left(1+i\right)^{n-2}+\ldots+R{(1+i)}^1+R{(1+i)}^0$

Where, R – Periodic receipt or payment, n – length of annuity, i – percent for the time period.

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

FVIFAi,n stands for the future interest factor of an annuity at i percentage for n periods. It can be found from tables.

2. Present Value of an Annuity

Formula for present value of an annuity is

$PVAn=\frac{R}{\left(1+i\right)^1}+\frac{R}{\left(1+i\right)^2}+\ldots+\frac{R}{\left(1+i\right)^n}=R\left(PVIFAi,n\right)$

Where, R – Constant periodic flow, i – discount rate, PVIFAi,n – present value interest factor of an (ordinary) annuity at i percent for n periods.

Numerical Problems

[Watch Video for Solution of the Questions]

Q 1. Find the amount of an annuity if payment of Rs. 1000 is made annually for 5 years at interest rate of 10% compounded annually.

Q 2. Find the present value of a 5 year annuity of Rs. 10000 discounted at 10%.

Annuity – Present Value and Future Value