Question

You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4 percent per year, with the first payment of $60,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal

Answer 1

The question is incomplete. The complete question is :

You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4 percent per year, with the first payment of $60,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? (The interest rate is 12%.)

Solution :

Given data :

pv of growing annuity, i = 0.04

Rate of interest, r = 0.12

Therefore,

`$pv=(60000)/((1+r) ) + (60000(1+i))/((1+r)^2 ) + (60000(1+i)^2)/((1+r)^3 ) + ...+ (60000(1+r)^(24))/((1+r)^(25) ) $`

`$pv=((60000)/((1+r))\left(1-\left((1+i)/(1+r)\right)^(25)\right))/(1-\left((1+i)/(1+r)\right))$`

`$pv=((60000)/((1.12))\left(1-\left((1.05)/(1.12)\right)^(25)\right))/(1-\left((1.04)/(1.12)\right))$`

`$pv = (60000)/(1.12) * 11.80461368$`

`$pv = \$ 632390.0191$`

pv = $ 632390.02 (rounding off)