Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Justin deposited $4000 into an account with 5.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have inthe account after 10 years?Do not round any intermediate computations, and round your answer to the nearest cent.

Justin Deposited 4000 Into An Account With 55 Interest Compounded Semiannually Assuming That No Withdrawals Are Made How Much Will He Have Inthe Account After 1 class=

Sagot :

First, divide the annual interest rate by 2 to find the semiannual interest rate:

[tex]\frac{5.5}{2}=2.75[/tex]

Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.

Each period, the initial investment gets multiplied by a factor of:

[tex]1+\frac{2.75}{100}=1+0.0275=1.0275[/tex]

Over 20 semiannual periods, the initial investment will get multiplied by a factor of:

[tex]1.0275^{20}[/tex]

Therefore, after 10 years, the amount of money in the account is:

[tex]\begin{gathered} 4000\times(1.0275)^{20}=4000\times1.7204\ldots \\ =6881.7137\ldots \end{gathered}[/tex]

To the nearest cent, the amount of money in the account will be:

[tex]6881.71[/tex]

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.