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