Pregunta
If
is invested at
annual simple interest, how long does it take to be worth
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Ask by Garza Tran. in the United States
Dec 08,2024
Solución de inteligencia artificial de Upstudy
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It takes 8 years for the investment to grow to $7000.
Solución
To find out how long it takes for an investment to grow from $5000 to $7000 at a 5% annual simple interest rate, we can use the formula for simple interest:
where:
-
is the amount of money accumulated after n years, including interest. -
is the principal amount (the initial amount of money). -
is the annual interest rate (decimal). -
is the time the money is invested for in years.
In this case:
We need to solve for
. Plugging in the values, we have:
Now, divide both sides by 5000:
This simplifies to:
Next, subtract 1 from both sides:
Now, divide both sides by 0.05 to solve for
:
Thus, it takes 8 years for the investment to grow from $5000 to $7000 at a 5% annual simple interest rate.
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Bonus Knowledge
To find out how long it takes for an investment of $5000 to grow to $7000 at a 5% annual simple interest rate, we can use the formula for simple interest:
, where
is the amount of money accumulated after n years, including interest,
is the principal amount (the initial investment),
is the rate of interest per year, and
is the time in years.
Plugging in the values, we have:
Dividing both sides by 5000:
Subtracting 1 from both sides:
Dividing both sides by 0.05:
So it takes 8 years for the investment to grow to $7000!
In ancient times, interest was often used as a means of growth for wealth, with rates and agreements documented on clay tablets in Mesopotamia. The concept of simple interest formed the basis of many economies, allowing merchants to finance their goods and expand their businesses, leading to the development of trade routes and the wealthy civilizations we read about today.
Understanding simple interest is not just academic; it applies in everyday scenarios like savings accounts, loans, and investments. Knowing how interest accrues helps you make informed financial decisions, whether you’re planning to save for a vacation, buy a car, or invest for retirement. Always double-check the terms of your interest rates and how they apply to your goals!

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