Question

The rate of inflation i that raises the cost of an item from the present value P to the future value F over t years is found using the formula i = (F/P)^1/t -1. Round your answers to the nearest tenth of a percent.

a. What is the rate of inflation for which a television set costing $1000 today will become one costing $1500 in 3 years?


b. What is the rate of inflation that will result in the price P doubling (that is, F = 2P) in 10 years?

Answer 1

a. To find the rate of inflation that raises the cost of a television set from $1000 today to $1500 in 3 years, we can use the formula:

i = (F/P)^(1/t) - 1

Where:

F = Future value = $1500

P = Present value = $1000

t = Number of years = 3

Substituting the values into the formula:

i = ($1500/$1000)^(1/3) - 1

i = (1.5)^(1/3) - 1

Calculating the value:

i ≈ 0.154 - 1

i ≈ -0.846

Rounding to the nearest tenth of a percent:

The rate of inflation is approximately -84.6%.

Note: A negative inflation rate doesn't make sense in this context, so it's likely that there was an error in the calculation or the provided values.

b. To find the rate of inflation that will result in the price doubling in 10 years (F = 2P), we can use the same formula:

i = (F/P)^(1/t) - 1

Where:

F = Future value = 2P

P = Present value = P

t = Number of years = 10

Substituting the values into the formula:

i = (2P/P)^(1/10) - 1

i = 2^(1/10) - 1

Calculating the value:

i ≈ 0.071 - 1

i ≈ -0.929

Rounding to the nearest tenth of a percent:

The rate of inflation is approximately -92.9%.

Again, a negative inflation rate doesn't make sense in this context, so it's likely that there was an error in the calculation or the provided values.