A bank features a savings account that has an annual percentage rate of $5.7 \%$ with interest compounded annually. Makayla deposits $\$ 6,500$ into the account. How much money will Makayla have in the account in 1 year? Answer = $\$ \square$ . Round answer to the nearest penny. What is the annual percentage yield (APY) for the savings account? $APY=$ $\square$ \%. Round to the nearest hundredth of a percent.
Answer (2)
Calculate the amount of money after 1 year using the compound interest formula: A = P ( 1 + r ) t , where P = 6500 , r = 0.057 , and t = 1 .
Substitute the values into the formula: A = 6500 ( 1 + 0.057 ) 1 = 6500 ( 1.057 ) = 6870.5 .
Determine the annual percentage yield (APY), which is equal to the annual interest rate since the interest is compounded annually: A P Y = 5.7% .
State the final answers: The amount of money Makayla will have in the account in 1 year is $6 , 870.50 , and the APY is 5.7% .
Explanation
Calculate the amount after 1 year First, we need to calculate the amount of money Makayla will have in the account after 1 year. We use the formula for compound interest, which is: A = P ( 1 + r ) t where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (as a decimal).
t is the number of years the money is invested for.
Calculate the amount In this case, we have:
P = $6 , 500
r = 5.7% = 0.057
t = 1 year Plugging these values into the formula, we get: A = 6500 ( 1 + 0.057 ) 1 A = 6500 ( 1.057 ) A = 6870.5 So, Makayla will have $6 , 870.50 in the account after 1 year.
Determine the APY Next, we need to find the annual percentage yield (APY). Since the interest is compounded annually, the APY is simply the annual interest rate. Therefore, the APY is 5.7% .
Final Answer Therefore, the amount of money Makayla will have in the account in 1 year is $6 , 870.50 , and the annual percentage yield (APY) for the savings account is 5.7% .
Examples
Understanding compound interest is crucial for making informed financial decisions. For example, when planning for retirement, knowing the APY helps you estimate how much your savings will grow over time. Similarly, when comparing different savings accounts, the APY allows you to determine which account offers the best return on your investment. This knowledge empowers you to make strategic choices and maximize your financial growth.
Makayla will have $6,870.50 in her account after 1 year, with an annual percentage yield (APY) of 5.7%.
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