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`

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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`

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