Question

find the cost of each item in 14 years, assuming an annual inflation rate of 5% (compounded annually). (round your answers to the nearest cent.)
(a) movie admission, $9.00
$
(b) cd, $16.65
$
(c) textbook, $100.00
$
(d) electricity bill, $155.00
$

Explanation:

Step1: Use the compound - interest formula

The compound - interest formula for inflation is \(A = P(1 + r)^t\), where \(P\) is the present value, \(r\) is the annual interest rate (as a decimal), and \(t\) is the number of years. Here, \(r=0.05\) and \(t = 14\).

Step2: Calculate for the electricity bill (\(P=\$155\))

Substitute \(P = 155\), \(r=0.05\), and \(t = 14\) into the formula \(A=P(1 + r)^t\).

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We know that \((1.05)^{14}\approx1.97993\) (using a calculator or the formula \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\) with \(a = 1\), \(b=0.05\), \(n = 14\)).

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Answer:

\(\$306.89\)