CAN ANYONE PLEASE ANSWER PROBLEM #74? You plan to retire in 30 years and want to

Question

CAN ANYONE PLEASE ANSWER PROBLEM #74?

You plan to retire in 30 years and want to accumulate enough by then to provide yourself with $30,000 a year for 15 years. If the interest rate is 10%, how much must you accumulate by the time you retire? How much must you save each year until retirement in order to finance your retirement consumption? Now you remember that the annual inflation rate is 4%. If a loaf of bread costs $1 today, what will it cost by the time you retire? You really w ant to consume $30,000 a year in real dollars during retirement and wish to save an equal real amount each year until then. What is the real amount of savings that you need to accumulate by the time you retire? Calculate the required preretirement real annual savings necessary to meet your consumption goals. Compare with your answer to (b). Why is there a difference? What is the nominal value of the amount you need you save during the first year? (Assume the savings are put aside at the end of each year.) The thirtieth year? Redo pan (a) of Practice Problem 64, but now assume that the inflation rate over the next 50 years will average 5%. (L06) What is the real annual savings the couple must set aside? How much do they need to save in nominal terms in the first year? How much do they need to save in nominal terms in the last year? What will be their nominal expenditures in the first year of retirement? The last?

Explanation / Answer

(a) Let the amount accumulated be P
Annual amount(A)= $30,000
Time(t)= 15 yrs
Rate(r)= 10%
This problem is similar to the repayment of a loan in equal instalments.

P= A(1-1/(1+r)t)/r

P=30000(1-1/1.115)/0.1 = $228,182

(b) Future value of an annuity is given by,

FV= A [(1+r)n-1]/r

where A is the annuity, r= rate of interest and n is the time

FV= $228,182

A = FV*r/[(1+r)n-1] = 228,182*0.1/[(1+0.1)30-1]= $1387.17

So, annual savings= $1387.17

(c) FV of $1 = 1(1+0.04)30 = $3.24

The loaf of bread will cost $3.24 by the time of retirement.

(d) Considering inflation,

P= A(1-[(1+i)/(1+r)]t)/r-i

i=4%, A= $30,000, r= 10%

P=30000(1-(1.04/1.1)15)/(0.1-0.04) = $284,434

(e) Considering inflation,

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

FV= $284,434

A= 284434*(0.06)/{(1.1/1.04)30-1}= $3896

The difference is due to inflation, i.e. the declining value of money

(f) Nominal value of 1st year savings= 3896/(1+0.04) = $3746

Nominal value of 30th year savings= 3896/(1+0.04)30 = $1201

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