You plan to retire in 30 years. Beginning in 31 years from now you wish to...

You plan to retire in 30 years. Beginning in 31 years from now you wish to have an annual retirement

income of $80,000 / year as measured in today’s dollars. The inflation rate is assumed to be 2.5%. Each

year in retirement you wish to have your retirement income grow by 3% per year. You plan on living for

35 years in retirement. Starting in one year from now you are going to make annual deposits into a

savings account. Your savings payments are expected to grow by 5% per year. You will make 30

payments into your retirement account. The discount rate is 9%. How much must your first savings

amount be in order to achieve your retirement goal

Solutions

Expert Solution

Given, Inflation rate (i)= 2.5%. Amount required per year, commencing in 31 years=$80,000

Therefore first payment required after retirement= $80,000*(1+i)^31 = $80,000*1.025^31 = $80,000*2.150007= $172,000.54

Rate of growth required after retirement= 3%

Therefore, fund required for payment for 35 in retirement as stated is the present value of a growing annuity arrived at $2,471,532.94 as follows:

In order to accumulate this amount, first payment required to annual deposit plan for 30 years is $11,051.22 as follows:

jeff jeffy answered 2 months ago

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