Answer:
X = 1523
Explanation
Perpetuity due = (C/r) + C. Where Annual payment C =500, Annual effective interest rate = 10%
Perpetuity due = (500/10%) + 500 = 5500
Value of perpetuity due will remain same after 10 years
Money in saving account can be calculated with FV of an Annuity due formula
FV = C*(1+r) *{(1+r) ^n−1} / r
Where n = 10 years
FV = 500*(1+10%) * {(1+10%)^10 - 1} / 10%
FV = 500*1.10 * [1.10^10 - 1 / 0.10}
FV = 550 * 1.5937424601/0.10
FV = 550 * 15.937424601
FV = 8765.58353055
FV = 8766
Total proceeds = 5500 + 8766 = 14266
Now this proceed is the present value for annual payment of X calculation . Formula of the present value (PV) of annuity due: PV = X * [1- (1+r) ^-n / r] * (1+r)
: Where PV = 14266, Annuity payment X = ?, Interest rate r = 10%, Period of annuity = 20 years.
1.10^-20
PV = X * [1- (1+r)^-n / r] * (1+r)
14266 = X * (1 - (1+10%)^-20 / 10%) * (1+10%)
14266 = X * [1 - 0.14864362802/0.10]*1.10
14266 = X * [8.5135637198*1.10]
14266 = X * 9.3649
X = 14266 / 9.3649
X = 1523.347820051469
X = 1523
