ENG 106
Homework #4 Solutions
Winter 2012
4.7 An annuity provides for 10 consecutive endofyear payments of $8,500. The average general inflation rate is
estimated to be 5% annually, and the market interest rate is 12% annually. What is the annuity worth in terms of a
single equivalent amount of today’s dollars?
Today’s dollars = use market interest rate
P = A (P/A,
ι
, N) = 8500 ( P/A, 12 %, 10 ) = 8500 * (5.6502) = $48,027.
4.10 The purchase of a car requires a $12,000 loan to be repaid in monthly installments for four years at 12%
interest compounded monthly. If the general inflation rate is 6% compounded monthly, find the actual and constant
dollar value of the 20
th
payment of this loan.
N = monthly * 4 years = 48 periods. i = 12% = 1% monthly, f
= 6% = .5% monthly,
P = 12000
A = P (A/P, interest rate, N), where for actual dollars, A
x
= A
20
A
20
= 12000 * (A/P, 1%, 48) = 12000 * (.0263) = $315.60 in actual dollars.
A
n
*[(P/F , inflation rate , n)] = Constant Dollars. = A’
20
A’
20
= A
20
*[P/F, .5% , 20)] = $315.60*.9051 = $285.65 in constant (yearzero) dollars.
#3 Begin with an equal payment series in constant dollars of A’ = $1000 at the end of each of three years.
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 Spring '12
 fizali
 Time Value Of Money, Net Present Value, general inflation rate

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