1. Find Regular Deposit
(PMT Amount) C = ?
Interest Rate i = 10%, Time n = 5 Year, Present value PV = 4169.87,
Deposit Frequency = at the beginning (Annuity Due) of every Year (1/year)
for Present value of Annuity Due method

Solution:
`i=10%=0.1` per year (Interest rate)

`n=5` years (Number of periods)

`PV=4169.87` (Present value)

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

`:.4169.87=C*[(1-(1+0.1)^-5)/(0.1)]*(1+0.1)`

`:.4169.87=C*[(1-(1.1)^-5)/(0.1)]*1.1`

`:.4169.87=C*[(1-0.6209)/(0.1)]*1.1`

`:.4169.87=C*[3.79]*1.1`

`:.C=4169.87/(3.79*1.1)`

`:.C=1000`

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2. Find Regular Deposit
(PMT Amount) C = ?
Interest Rate i = 10%, Time n = 3 Year, Present value PV = 13677.69,
Deposit Frequency = at the beginning (Annuity Due) of every Year (1/year)
for Present value of Annuity Due method

Solution:
`i=10%=0.1` per year (Interest rate)

`n=3` years (Number of periods)

`PV=13677.69` (Present value)

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

`:.13677.69=C*[(1-(1+0.1)^-3)/(0.1)]*(1+0.1)`

`:.13677.69=C*[(1-(1.1)^-3)/(0.1)]*1.1`

`:.13677.69=C*[(1-0.7513)/(0.1)]*1.1`

`:.13677.69=C*[2.49]*1.1`

`:.C=13677.69/(2.49*1.1)`

`:.C=5000`

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