A couple will retire in 50 years they plan to spend in today

A couple will retire in 50 years; they plan to spend (in today\'s dollars) about $ should last about 25 years. They over the next 75 years is expected to average 5%. 30,000 a year in retirement, which inflation rate believe that they can earn 8% interest on retirement savings. The o. What is the real annual savings the couple must set aside? Assume they will discontinue sa retire. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Answer is complete and correct. S 4,902.40 b. How much do they need to save in nominal terms in the first year? (Do not round intermediate calculations Round your answer to 2 decimal places.) Answer is complete and correct. Nominal savings 5,147.52 c. How much do they need to save in nominal terms in the last year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) 3 Answer is complete but not entirely correct. S 51,064 30

Solution

a )First of all let us calculate real rate of interest

Real rate of interest = (1+ nominal rate of interest)/(1+inflation rate) - 1

=(1.08)/(1.05) - 1

=1.0286-1

=2.86%

Now let us calculate the the mount required at end of 50th year

PV(annuity) = A[1-(1/(1+r)^n / r ]

=30000[1-(1/1.0286)^25 / 0.0286]

=30000[1-0.4941 / 0.0286]

=30000[0.50587/0.0286]

=30000*17.6879

=530637.9054$

Now let us calculate Annual savings

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

=530637.9054 = A[(1.0286)^50-1/0.0286]

=53067.9054 = A[108.240555]

A = 4902.4$

b) Amount they need to save in first year in nominal terms = 4902.4*1.08/1.0286

=5147.52$

c) Amount they need to save in first year in nominal terms will be same as amount to be saved in first year, Thus answer 5147.52$