Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Answer:
Yazmin needs an interest rate of 5.45%.
Step-by-step explanation:
Compound Interest Formula (Yearly)
To know how much money an account makes from its initial deposit, the interest rate and, the number years that elapsed, a formula can be used to calculate as such.
[tex]A=P\left(1+r)^t[/tex],
where P is the initial amount that's placed into the account, r is the interest rate in decimal form, t is the time that passes in years and A is the value of the account at time t years.
Solving the Problem
Yazmin want's her $50,000 to grow to $85,000 in 10 years, meaning that she'll need to open a yearly compound interest account.
The problem asks for the value of r in percentage form, to do that we must find the value of r in its original decimal form.
Plugging the appropriate values and variables into the equation we have,
[tex]85000=50000(1+r)^1^0[/tex].
Now, we rearrange the equation to isolate and compute the r variable!
[tex]\dfrac{85000}{50000} =(1+r)^1^0[/tex]
[tex]1.7=(1+r)^1^0[/tex]
[tex]\sqrt[10]{1.7} =1+r[/tex]
[tex]\sqrt[10]{1.7} -1=r[/tex]
[tex]0.0545=r[/tex]
To transform the interest rate into percentage form we move the decimal point two places to the right. So, the interest rate Yazmin needs is 5.45%.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.