Final answer:
Rosie's balance after 6 years with compound interest is found using the compound interest formula A = P(1 + r/n)^(n.t). Inflation affects the future buying power of money, as seen with Rosalie's anticipated $20,000 payment. Simple interest calculations for a loan differ from compound interest, using the formula I = P*r*t.
Step-by-step explanation:
Calculating Compound Interest:
Rosie deposits P5500 into her savings account and wants to know her balance after earning 7.5% compound interest for 6 years. To calculate the future value of her investment, we use the formula for compound interest which is
A = P(1 + r/n)(n.t). Let's plug in the values: P = 5500 (the principal amount), r = 0.075 (the annual interest rate in decimal form), n = 1 (since it's compounded yearly), and t = 6 (the number of years).
After calculating this, A = 5500(1 + 0.075/1)(1*6) = 5500(1.075)6. The balance after 6 years would therefore be the result of this calculation. Make sure to use a calculator to finish this calculation.
Understanding Inflation's Impact on Future Value:
Separately, to understand the buying power of a future sum of money, we consider inflation. For example, Rosalie the Retiree will receive a one-time payment of $20,000 in 16 years, but due to an annual inflation rate of 6%, we must calculate how much less the $20,000 will be worth in today's dollars. We would calculate the future price level and adjust the $20,000 accordingly to find its present value and determine the real buying power when Rosalie retires.
Simple Interest Comparisons:
In other scenarios where simple interest is applied to a loan, different calculations are made. For example, the total interest on a $5,000 loan with a simple interest rate of 6% over three years can be found using the simple interest formula I = Prt, where P is the principal, r is the rate, and t is the time in years. Similarly, if $500 is received as simple interest from a $10,000 loan over five years, we can work backwards to calculate the interest rate charged.