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
Solution:
`C=1000` (Cash flow per year)
`i=10%=0.1` per year (Interest rate)
`n=5` years (Number of periods)
Now, Present value (Annuity Due) formula is
`PV_("Annuity Due")=C*[(1-(1+i)^(-n))/(i)]*(1+i)`
`=1000*[(1-(1+0.1)^-5)/(0.1)]*(1+0.1)`
`=1000*[(1-(1.1)^-5)/(0.1)]*(1.1)`
`=1100*[(1-(1.1)^-5)/(0.1)]`
`=1100*[(1-0.6209)/(0.1)]`
`=1100*3.79`
`=4169.87`
Calculating each payment present value individually and then adding them all
| `0^(th)` year 1000's present value `=1000/(1.1)^0` | `=1000` |
| `1^(st)` year 1000's present value `=1000/(1.1)^1` | `=909.09` |
| `2^(nd)` year 1000's present value `=1000/(1.1)^2` | `=826.45` |
| `3^(rd)` year 1000's present value `=1000/(1.1)^3` | `=751.31` |
| `4^(th)` year 1000's present value `=1000/(1.1)^4` | `=683.01` |
| Total present value | `=4169.87` |
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
Solution:
`C=5000` (Cash flow per year)
`i=10%=0.1` per year (Interest rate)
`n=3` years (Number of periods)
Now, Present value (Annuity Due) formula is
`PV_("Annuity Due")=C*[(1-(1+i)^(-n))/(i)]*(1+i)`
`=5000*[(1-(1+0.1)^-3)/(0.1)]*(1+0.1)`
`=5000*[(1-(1.1)^-3)/(0.1)]*(1.1)`
`=5500*[(1-(1.1)^-3)/(0.1)]`
`=5500*[(1-0.7513)/(0.1)]`
`=5500*2.49`
`=13677.69`
Calculating each payment present value individually and then adding them all
| `0^(th)` year 5000's present value `=5000/(1.1)^0` | `=5000` |
| `1^(st)` year 5000's present value `=5000/(1.1)^1` | `=4545.45` |
| `2^(nd)` year 5000's present value `=5000/(1.1)^2` | `=4132.23` |
| Total present value | `=13677.69` |
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
