Present value of Annuity Due calculator

SolutionHelp

1. Find Present value PV = ?
Regular Deposit
(PMT Amount) C = 1000, Interest Rate i = 10%, Time n = 5 Year,
Deposit Frequency = at the beginning (Annuity Due) of every Year (1/year)
for Present value of Annuity Due method

2. Find Present value PV = ?
Regular Deposit
(PMT Amount) C = 5000, Interest Rate i = 10%, Time n = 3 Year,
Deposit Frequency = at the beginning (Annuity Due) of every Year (1/year)
for Present value of Annuity Due method

Example

C=1000 $C=1000$ (Cash flow per year)

i=10%=0.1 $i=10%=0.1$ per year (Interest rate)

n=5 $n=5$ years (Number of periods)

Now, Present value (Annuity Due) formula is
PVAnnuity Due=C⋅[1-(1+i)-ni]⋅(1+i) $PV_("Annuity Due")=C*[(1-(1+i)^(-n))/(i)]*(1+i)$

=1000⋅[1-(1+0.1)-50.1]⋅(1+0.1) $=1000*[(1-(1+0.1)^-5)/(0.1)]*(1+0.1)$

=1000⋅[1-(1.1)-50.1]⋅(1.1) $=1000*[(1-(1.1)^-5)/(0.1)]*(1.1)$

=1100⋅[1-(1.1)-50.1] $=1100*[(1-(1.1)^-5)/(0.1)]$

=1100⋅[1-0.62090.1] $=1100*[(1-0.6209)/(0.1)]$

=1100⋅3.79 $=1100*3.79$

=4169.87 $=4169.87$

Calculating each payment present value individually and then adding them all

0th $0^(th)$ year 1000's present value =1000(1.1)0 $=1000/(1.1)^0$	=1000 $=1000$
1st $1^(st)$ year 1000's present value =1000(1.1)1 $=1000/(1.1)^1$	=909.09 $=909.09$
2nd $2^(nd)$ year 1000's present value =1000(1.1)2 $=1000/(1.1)^2$	=826.45 $=826.45$
3rd $3^(rd)$ year 1000's present value =1000(1.1)3 $=1000/(1.1)^3$	=751.31 $=751.31$
4th $4^(th)$ year 1000's present value =1000(1.1)4 $=1000/(1.1)^4$	=683.01 $=683.01$
Total present value	=4169.87 $=4169.87$