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?

Question

Valery Boone

Business

14 November, 01:50

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?

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Imani Norton · Answer 1

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