Question

PLEASE HELP I AM FAILING

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. The rate of inflation for which a television set costing $1000 today will become one costing $1500 in 3 years is approximately 14.5%.

b. The rate of inflation that will result in the price doubling (F = 2P) in 10 years is approximately -92.8%.

Explanation:

a. To find the rate of inflation for a television set costing $1000 today that will become one costing $1500 in 3 years, we can use the formula:

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

Given:

P = $1000 (present value)

F = $1500 (future value)

t = 3 years

Substituting these values into the formula:

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

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

Calculating the value inside the parentheses:

i = 1.1447 - 1

i ≈ 0.1447

Therefore, the rate of inflation is approximately 14.5%.

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

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

Given:

F = 2P (future value is double the present value, P)

t = 10 years

Substituting the values into the formula:

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

i = 2^(1/10) - 1

Calculating the value inside the parentheses:

i ≈ 0.0718 - 1

i ≈ -0.9282

Therefore, the rate of inflation that would result in the price doubling in 10 years is approximately -92.8%. Note that a negative inflation rate implies deflation, which means the prices are decreasing rather than increasing.