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A couple will retire in 50 years; they plan to spend about $30,000 a year (in current dollars) in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. The inflation rate over the next 75 years is expected to average 5%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Required:
a. What is the real annual savings the couple must set aside?
b. How much do they need to save in nominal terms in the first year?
c. How much do they need to save in nominal terms in the last year?
d. What will be their nominal expenditures in the first year of retirement?
e. What will be their nominal expenditures in the last year of retirement?

Respuesta :

fichoh

Answer:

4908.3650 ;

5153.7832 ;

56286.1837 ;

344021.993 ;

1164980.5

Explanation:

Real interest rate (r) :

((1 + 8%) ÷ (1 + 5%)) - 1

(1.08 ÷ 1.05) - 1

= 0.02857

Present value :

30000 *[(1/r) - (1/(r * (1+r)^n))

30000*[(1/0.02857) - (1/(0.02857 * (1.02857)^25))

30000* 17.693887

= 530816.61

Cashflow (C)

530816.61 ÷ [(1.02857^50 - 1) / 0.02857]

530816.61 ÷ 108.14530

= 4908.3650

B.)

Nominal saving (1st year)

4908.3650 * 1.05

= 5153.7832

C.)

Nominal saving (Last year)

4908.3650 * 1.05^50

= 56286.1837

D.)

Nominal expenditure (1st year)

30000 * 1.05^50

= 344021.993

E.)

Nominal expenditure (last year)

30000 * 1.05^75

= 1164980.5

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