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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%.
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