Question

Problem (5): An investment pays $ 30,000 after five years. a) If the annual inflation rate is 8%, what is the real value of the $30,000 in today's dollars? b) If the annual inflation rate is 8% and the real interest rate is 12%, what is the present worth of the investment return? c) What Actual-dollar interest rate is equivalent to a real interest rate of 12% when the annual inflation rate is 8% d) Compute the present worth using the Actual dollar interest rate from part (C)?

Answer 1

a)

Real value of $ 30,000 in today's dollars = $ 30,000 $\times$ ( 1 + inflation rate )^-n = $ 30,000 $\times$ ( 1 + 0.08)^-5

Real value of $ 30,000 in today's dollars = $ 20,417.50

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b)

Nominal interest rate = Real interest rate + Inflation rate

Nominal interest rate = 12% + 8%

Nominal interest rate = 20%

$30,000 Present worth of the investment return = 7 (1 +0.20) 5

Present worth of the investment return = $ 12,056.33

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c)

Actual dollar interest rate = [ (1 + 0.12 ) $\times$ ( 1 + 0.08) - 1 ]

Actual dollar interest rate = 20.96%

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d)

Present worth = $30,000 (1 + 0.2096)

Present worth = $ 11,585.44