Question

If patty shoemaker estimates that her $100 weekly grocery bill will increase at an annual inflation rate of 5%, what should her weekly grocery bill be in 4 years?

a) $121.60
b) $131.60
c) $121.90
d) $131.30

Answer 1

Using the compound interest formula, Patty Shoemaker's weekly grocery bill is expected to rise from $100 to approximately $121.55 in 4 years, due to an annual inflation rate of 5%. The closest given option is (a) $121.60.

Step-by-step explanation:

To estimate the increase in Patty Shoemaker's weekly grocery bill due to a consistent annual inflation rate of 5%, we can use the formula for compound interest. This is because inflation compounds similarly, affecting not just the original amount but also the increases from previous years. The formula to calculate the future value after inflation is:

FV = PV (1 + r)^n

Where FV is the future value, PV is the present value or current amount, r is the annual rate of inflation, and n is the number of years.

For Patty's groceries:

• PV = $100
• r = 0.05 (5% expressed as a decimal)
• n = 4

Plugging these values into the formula, we get:

FV = 100 * (1 + 0.05)^4

FV = 100 * (1.21550625)

FV = $121.55

The closest option to $121.55 is $121.60, so the final answer is (a) $121.60.