Question

You anticipate that you will need $1,500,000 when you retire 30 years from now. You just join a new firm and your first annual salary is $100,000 to be received one year from today. You also received one time signing bonus of $50,000 today. You decided that you will put all you signing bonus into your account plus you will contribute $X every year starting next year for the next 29 years. In other words, after your initial deposit of $50,000, your first payment will be made on year 1 and last payment will be on year 29. How much is $X if you want to have $1,500,000 in Year 30. Assume that interest rate is 8% , compounded annual during this duration.

a. $1,388,888.89

b. $1,288.,888.89

c. $106,159.09

d. $98,150.35

e. $8,878.15

Answer 1

Present value is $50,000

Interest rate (i)= 8% compounded annually

This Amount will be in deposit until 30 years. So time (n) = 30

Future value of Present value formula = Present value*(1+i)^n

50000*(1+8%)^30

503132.8445

Future value of $50,000 is $503132.85

We require $1500000 at 30 years

Out of which furure value of $50,000 is received as $503132.84

Balance Future value required= 1500000-503132.84= 996,867.16

P = $X Sum deposited for (n) = 29 years

First Sum is deposited next year and last deposit is in 29 years. So

Future value of annuity due formula = P *(1+i)*((1+r)^n -1) / r

996867.16= X*((1+8%)^29-1)/8%

996867.16= X* 112.2832111

X = 8878.149687

So, Amount required to be deposit annually is $8878.15

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