Find the final amount of money in an account if $600 is deposited at 7.5% interest compounded semi-annually and the money is left for 5 years.
Answer (2)
Use the compound interest formula: A = P ( 1 + n r ) n t .
Plug in the given values: P = 600 , r = 0.075 , n = 2 , and t = 5 .
Calculate the final amount: A = 600 ( 1 + 2 0.075 ) 2 × 5 ≈ 867.04 .
The final amount in the account after 5 years is 867.04 .
Explanation
Understanding the Problem We are asked to find the final amount in an account where an initial deposit of $600 is made, with an annual interest rate of 7.5% compounded semi-annually, for a period of 5 years. We will use the compound interest formula to solve this problem.
Identifying the Formula and Variables The formula for compound interest is: A = P ( 1 + n r ) n t Where:
A is the final amount
P is the principal amount ($600)
r is the annual interest rate (7.5% or 0.075)
n is the number of times the interest is compounded per year (semi-annually means 2 times per year)
t is the number of years (5 years)
Plugging in the Values Now, let's plug in the values into the formula: A = 600 ( 1 + 2 0.075 ) 2 × 5 A = 600 ( 1 + 0.0375 ) 10 A = 600 ( 1.0375 ) 10
Calculating the Exponent Now, we calculate ( 1.0375 ) 10 :
( 1.0375 ) 10 ≈ 1.44506
Calculating the Final Amount Next, we multiply this by the principal amount: A = 600 × 1.44506 A ≈ 867.036
Rounding the Answer Finally, we round the answer to two decimal places: A ≈ 867.04 So, the final amount in the account after 5 years is approximately $867.04.
Examples
Understanding compound interest is crucial in personal finance. For instance, when planning for retirement, knowing how your investments grow over time with compound interest helps you estimate your potential savings. Similarly, when taking out a loan, understanding the compound interest can help you calculate the total repayment amount and make informed decisions about borrowing. Compound interest is also applicable in various financial instruments like bonds, mutual funds, and savings accounts, making it a fundamental concept for financial literacy.
The final amount in the account after 5 years, with a $600 deposit at 7.5% interest compounded semi-annually, is approximately $867.04. This is calculated using the compound interest formula. After substituting the values and performing the calculations, we arrive at the result.
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