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You are planning to retire in twenty years

Finance

You are planning to retire in twenty years. You'll live ten years after retirement. You want to be able to draw out of your savings at the rate of $10,000 per year. How much would you have to pay in equal annual deposits until retirement to meet your objectives? Assume interest remains at 9% annually. 

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We can calculate the present value by using the following formula in excel:-

=-pv(rate,nper,pmt,fv)

Here,

PV = Present value

Rate = 9%

Nper = 10 periods

Pmt = $10,000

FV = $0

Substituting the values in formula:

= -pv(9%,10,10000,0)

= $64,176.58

If he have $64,176.58 in his account at the time of retirement, he can receive $10,000 over the next 10 years.

We can calculate the annual deposits by using the following formula in excel:-

=pmt(rate,nper,pv,-fv)

Here,

Pmt = Annual deposits

Rate = 9%

Nper = 20 periods

PV = $0

FV = $64,176.58

Substituting the values in formula:

= pmt(9%,20,0,-64176.58)

= $1,254.43

If he deposits $1,254.43 over the next 20 years, he can have $64,176.58 at the time of retirement.

So, you have to pay $1,254.43 in equal annual deposits to meet the goal.