Jason invested $360 in an account paying an interest rate of 5.4% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 9 years?
Answer (2)
Identify the principal (P), interest rate (r), compounding period (n), and time (t).
Apply the compound interest formula: A = P ( 1 + n r ) n t .
Substitute the given values: A = 360 ( 1 + 365 0.054 ) ( 365 ) ( 9 ) .
Calculate the future value and round to the nearest ten dollars: 590 .
Explanation
Understanding the Problem Let's analyze the problem. Jason invested $360 in an account with an interest rate of 5.4% compounded daily. We need to find out how much money will be in the account after 9 years, assuming no additional deposits or withdrawals are made. We will use the compound interest formula to solve this problem.
Identifying the Formula The compound interest formula is: A = P ( 1 + n r ) n t where:
A = Future value of the investment/loan, including interest
P = Principal investment amount (the initial deposit or loan amount)
r = Annual interest rate (as a decimal)
n = Number of times that interest is compounded per year
t = Number of years the money is invested or borrowed for
Assigning Values Now, let's identify the values for each variable:
P = $360
r = 5.4% = 0.054
n = 365 (compounded daily)
t = 9 years
Substituting Values Substitute the values into the formula: A = 360 ( 1 + 365 0.054 ) ( 365 ) ( 9 )
Calculating the Future Value Calculating the value inside the parentheses: 1 + 365 0.054 = 1 + 0.000147945 ≈ 1.000147945 Now, raise this to the power of (365 * 9) = 3285: ( 1.000147945 ) 3285 ≈ 1.625741554 Finally, multiply by the principal amount: A = 360 × 1.625741554 ≈ 585.2669595851036 So, the future value A is approximately $585.27.
Rounding to Nearest Ten Dollars We need to round the future value to the nearest ten dollars. Since $585.27 is closer to $590 than $580, we round up to $590.
Final Answer Therefore, after 9 years, the amount of money in the account, rounded to the nearest ten dollars, would be $590.
Examples
Compound interest is a powerful concept used in many real-life financial situations. For example, when you deposit money into a savings account, the bank pays you interest, which is often compounded. Similarly, when you take out a loan, the interest you owe is also calculated using compound interest. Understanding how compound interest works can help you make informed decisions about saving, investing, and borrowing money. It's also used in calculating the future value of investments, like retirement accounts, and in determining the cost of loans, such as mortgages.
After 9 years, Jason's investment of $360 at an interest rate of 5.4% compounded daily will grow to approximately $590. This amount is calculated using the compound interest formula, rounding to the nearest ten dollars. Therefore, the final amount he would have is $590.
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