Assume the inflation rate is \( 5 \% \) each year. This means one year later, the value of money will be \( 95 \% \) of what it worth the year before. This is called deflation. If you put \( \$ 900 \) under your mattress this year, what will be the estimated value (in today's dollars) in 5 years? \( \$ \) Round to the nearest cent. What is the total deflation rate over 5 years? \( \% \) Round to the nearest tenth of a percent.

If you put \$900 under your mattress for 5 years with a 5% inflation rate, the value of that money will decrease each year. To find the estimated value in today’s dollars, we can use the formula for present value: \[ PV = FV \times (1/(1+r)^n) \] where \(FV\) is the future value (\$900), \(r\) is the inflation rate (0.05), and \(n\) is the number of years (5). Calculating this gives: \[ PV = 900 \times (1/(1+0.05)^5) \approx 900 \times 0.7835 \approx 705.15 \] So, the estimated value in today's dollars will be approximately \$705.15. For the total deflation rate over 5 years, we can find the cumulative effect of the inflation rate. The formula for total deflation is: \[ Total\,Deflation\,Rate = \left(1 - (1+r)^n\right) \times 100 \] Substituting in the values: \[ Total\,Deflation\,Rate = \left(1 - (1+0.05)^5\right) \times 100 \approx 1 - 1.27628 \approx -0.27628 \times 100 \approx -27.6\% \] Therefore, the total deflation rate over 5 years is approximately -27.6%.