1. Find Future value FV = ?
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 Future 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, Future value (Annuity Due) formula is
`FV_("Annuity Due")=C*[((1+i)^n-1)/(i)]*(1+i)`
`=1000*[((1+0.1)^5-1)/(0.1)]*(1+0.1)`
`=1000*[((1.1)^5-1)/(0.1)]*(1.1)`
`=1100*[((1.1)^5-1)/(0.1)]`
`=1100*[(1.6105-1)/(0.1)]`
`=1100*6.11`
`=6715.61`
Calculating each payment future value individually and then adding them all
| `5^(th)` year 1000's future value in 1 year `=1000*(1.1)^1` | `=1100` |
| `4^(th)` year 1000's future value in 2 year `=1000*(1.1)^2` | `=1210` |
| `3^(rd)` year 1000's future value in 3 year `=1000*(1.1)^3` | `=1331` |
| `2^(nd)` year 1000's future value in 4 year `=1000*(1.1)^4` | `=1464.1` |
| `1^(st)` year 1000's future value in 5 year `=1000*(1.1)^5` | `=1610.51` |
| Total future value | `=6715.61` |
2. Find Future value FV = ?
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 Future 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, Future value (Annuity Due) formula is
`FV_("Annuity Due")=C*[((1+i)^n-1)/(i)]*(1+i)`
`=5000*[((1+0.1)^3-1)/(0.1)]*(1+0.1)`
`=5000*[((1.1)^3-1)/(0.1)]*(1.1)`
`=5500*[((1.1)^3-1)/(0.1)]`
`=5500*[(1.331-1)/(0.1)]`
`=5500*3.31`
`=18205`
Calculating each payment future value individually and then adding them all
| `3^(rd)` year 5000's future value in 1 year `=5000*(1.1)^1` | `=5500` |
| `2^(nd)` year 5000's future value in 2 year `=5000*(1.1)^2` | `=6050` |
| `1^(st)` year 5000's future value in 3 year `=5000*(1.1)^3` | `=6655` |
| Total future value | `=18205` |
This material is intended as a summary. Use your textbook for detail explanation.
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