Aubrey invested $\$ 7,100$ in an account paying an interest rate of 5.6\% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 19 years? Answer Attempt 1 out of 100
Solution
Step 1 ：Given that Aubrey invested $7100 in an account paying an interest rate of 5.6% compounded quarterly, we are to find how much money would be in the account after 19 years assuming no deposits or withdrawals are made.
Step 2 ：We can find this by using the formula for future value (FV) in the case of compound interest: \(FV = P * (1 + r/n)^{nt}\), where: \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.
Step 3 ：Substituting the given values into the formula, we have: \(P = 7100\), \(r = 0.056\), \(n = 4\) (since interest is compounded quarterly), and \(t = 19\) years.
Step 4 ：Calculating the future value, we get: \(FV = 7100 * (1 + 0.056/4)^{4*19}\)
Step 5 ：Solving the above expression, we find that the future value is approximately $20420.
Step 6 ：Thus, the amount of money in the account after 19 years, to the nearest ten dollars, would be \(\boxed{20420}\).
