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A couple will retire in 50 years; they plan to spend about $22,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. a. If they make annual payments into a savings plan, how much will they need to save each year

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facundobuzzetti

Answer:

Annual deposit= $2,803.09

Explanation:

First, we need to calculate the monetary value at retirement:

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

A= annual payment

FV= {22,000*[(1.08^25) - 1]} / 0.08

FV= $1,608,330.68

Now, the annual deposit required to reach $1,608,330.68:

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

A= annual deposit

Isolating A:

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

A= (1,608,330.68*0.08) / [(1.08^50) - 1]

A= $2,803.09

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