Question

find the cost of each item in 15 years, assuming an annual inflation rate of 6% (compounded annually). (round your answers to the nearest cent.)
(a) movie admission, $10.00
$ 23.97
(b) cd, $16.25
$ 38.84
(c) textbook, $85.00
$ 203.71
(d) electricity bill, $125.00
$

Explanation:

Step1: Recall Compound Interest Formula

The formula for compound interest (which applies to inflation as it's a compound growth of cost) is $A = P(1 + r)^t$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. Here, $r = 0.06$, $t = 15$, and $P = 125.00$ for the electricity bill.

Step2: Substitute Values into Formula

Substitute $P = 125$, $r = 0.06$, and $t = 15$ into the formula: $A = 125(1 + 0.06)^{15}$.

Step3: Calculate $(1 + 0.06)^{15}$

First, calculate $1.06^{15}$. Using a calculator, $1.06^{15}\approx2.396558193$.

Step4: Multiply by Present Value

Multiply this result by 125: $A = 125\times2.396558193\approx299.57$.

Answer:

$\$299.57$