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Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. A ind the APY for the account. A $9000 deposit in an account with an APR of 4.3%. The balance in the account after 1 year is approximately $

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. A ind the APY for the account. A $9000 deposit in an account with an APR of 4.3%. The balance in the account after 1 year is approximately $

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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View an example | All parts showing Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $8000 deposit in an account with an APR of 4.7%. Use the compound interest formula for continuous compounding shown below, where A is the accumulated balance after Y years, P is the starting principal, and APR is the annual percentage rate expressed as a decimal. A=Pxe(APRXY) To find A after 1 year, substitute the values for P and APR given in the problem statement with Y= 1. Start by identifying the value of the starting principal, P. P = $8000 Write the interest rate in decimal notation. APR=0.047 Substitute P = $8000, Y = 1, and APR=0.047 into the compound interest formula for continuous compounding and simplify. A = Pxe(APRxY) = $8000x (0.047 x 1) = $8000 x 0.047 = $8384.98 A = Pxe(APRXY) = $8000x (0.047 x 5) = $8000 x 0.235 = $10,119.27 Therefore, the balance in the account after 1 year is $8384.98. Use the compound interest formula for continuous compounding to find the balance in the account after 5 years. The only value that changes from the 1 year balance is the amount of time, Y. Substitute P = $8000, Y = 5, and APR=0.047 into the formula and simplify. A = Pxe(APRxY) = $8000x (0.047 x 20) = $8000 x 0.94 = $20,479.84 C Therefore the balance in the account after 5 years is $10,119.27. To find the balance in the account after 20 years let Y=20. Substitute P = $8000, Y=20, and APR=0.047 into the formula and simplify. APY = relative increase = Substitute. Simplify. Evaluate and round to the nearest cent. APY = $384.98 $8000 Substitute. Simplify. Evaluate and round to the nearest cent. Therefore, the balance in the account after 20 years is $20,479.84. The annual percentage yield (APY) is the actual percentage by which a balance increases in one year. It can be found by using the formula below, where absolute increase is the amount of interest paid in one year, and the starting principal is the principal at the start of the year. x 100 X Substitute. Simplify. Evaluate and round to the nearest cent. Use the amount in the account after 1 year found earlier to be A = $8384.98, and the starting principal, P = $8000, to find the APY. Multiply by 100 to express as a percent and rounding to two decimal places. absolute increase starting principal ≈ 4.81% Therefore, the APY for the account is approximately 4.81%.
Transcribed Image Text:View an example | All parts showing Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $8000 deposit in an account with an APR of 4.7%. Use the compound interest formula for continuous compounding shown below, where A is the accumulated balance after Y years, P is the starting principal, and APR is the annual percentage rate expressed as a decimal. A=Pxe(APRXY) To find A after 1 year, substitute the values for P and APR given in the problem statement with Y= 1. Start by identifying the value of the starting principal, P. P = $8000 Write the interest rate in decimal notation. APR=0.047 Substitute P = $8000, Y = 1, and APR=0.047 into the compound interest formula for continuous compounding and simplify. A = Pxe(APRxY) = $8000x (0.047 x 1) = $8000 x 0.047 = $8384.98 A = Pxe(APRXY) = $8000x (0.047 x 5) = $8000 x 0.235 = $10,119.27 Therefore, the balance in the account after 1 year is $8384.98. Use the compound interest formula for continuous compounding to find the balance in the account after 5 years. The only value that changes from the 1 year balance is the amount of time, Y. Substitute P = $8000, Y = 5, and APR=0.047 into the formula and simplify. A = Pxe(APRxY) = $8000x (0.047 x 20) = $8000 x 0.94 = $20,479.84 C Therefore the balance in the account after 5 years is $10,119.27. To find the balance in the account after 20 years let Y=20. Substitute P = $8000, Y=20, and APR=0.047 into the formula and simplify. APY = relative increase = Substitute. Simplify. Evaluate and round to the nearest cent. APY = $384.98 $8000 Substitute. Simplify. Evaluate and round to the nearest cent. Therefore, the balance in the account after 20 years is $20,479.84. The annual percentage yield (APY) is the actual percentage by which a balance increases in one year. It can be found by using the formula below, where absolute increase is the amount of interest paid in one year, and the starting principal is the principal at the start of the year. x 100 X Substitute. Simplify. Evaluate and round to the nearest cent. Use the amount in the account after 1 year found earlier to be A = $8384.98, and the starting principal, P = $8000, to find the APY. Multiply by 100 to express as a percent and rounding to two decimal places. absolute increase starting principal ≈ 4.81% Therefore, the APY for the account is approximately 4.81%.
Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $9000 deposit in an account with an APR of 4.3%. The balance in the account after 1 year is approximately $ (Round to the nearest cent as needed.)
Transcribed Image Text:Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $9000 deposit in an account with an APR of 4.3%. The balance in the account after 1 year is approximately $ (Round to the nearest cent as needed.)
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APR stands for Annual Percentage Rate. It is a measure of the borrowing cost, expressed as a yearly rate. The APR includes the interest rate charged on the loan and any other fees or charges associated with the loan. The APR is typically higher than the interest rate because it takes into account all of the costs associated with the loan.

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