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A woman is planning to retire in 10 years. She wishes to deposit a regular amount every six months until she retires, so that beginning one year following retirement she will receive annual payments of $20,000 for the next 20 years. How much must be deposited every six months if the annual nominal interestra te is 8%, compounded semiannually?

Answer :

facundobuzzetti

Answer:

The deposit should be of $8,059.62

Explanation:

Giving the following information:

A woman is planning to retire in 10 years.

She wants to receive 20 annual payments of $20,000.

Interest rate= 8% compunded semiannually

To calculate the semiannual deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= semiannual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

FV= 20*20,000= 240,000

i= 0.08/2= 0.04

n= 10*2= 20

A= (240,000*0.04)/ [(1.04^20)-1]

A= $8,059.62

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