An individual wants to have $95,000 per year to live on when she retires in 30 years. The individual is planning on living for 20 years after retirement. If the investor can earn 6% during her retirement years and 10% during her working years, how much should she be saving during her working life

The amount she would be saving during her working life is  $1,089,64 and the deposit required for each year is $6,624.21

Explanation:

Solution

Given that:

The amount of income needed for retirement income = P×[1-(1÷(1+r)^n)]÷r

Now,

The Interest rate per annum  =6.00%

The Number of years = 2

The Number of compoundings per annum  = 1

The Interest rate per period ( r)=6.00%      

The period per payment (P)=$ 95,000

The Amount required for retirement income = 95000*[1-(1/(1+6%)^95000]/6% =$1,089,643        

Now,

Required deposit for every year (P)=FVA÷([(1+r)^n-1]÷r)

The Interest rate per annum= 10.00%

The Number of years= 30                                          

The number payments per per annum =1                                       The Interest rate per period ( r)=10.00%

The Number of periods (n)=30

Thus,

The Future value of annuity (FVA) = $1,089,643  

Hence the deposit required for each year is = 1089643/(((1+10%)^30-1)/10%)

= $6,624.21

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