Yvonne put $4,000 in a savings account. At the end of 3 years, the account had earned $960 in simple interest.
How much does she have in her account at the end of 3 years?
At what annual simple interest rate did the account grow? Show your work.
How many more dollars would she have in her account if the interest rate were 1% greater? Show your work.
To calculate the total amount in Yvonne's savings account at the end of 3 years, we need to add the original principal to the interest earned.
Total amount = principal + interest
Total amount = $4,000 + $960
Total amount = $4,960
To calculate the simple interest rate, we need to use the formula:
Interest = Principal x Rate x Time
We already know the values for Principal, Interest, and Time, so we can rearrange the formula to solve for Rate:
Rate = Interest / (Principal x Time)
Rate = $960 / ($4,000 x 3)
Rate = $960 / $12,000
Rate = 0.08 or 8%
So the account grew at an annual simple interest rate of 8%.
To calculate how much more Yvonne would have in her account if the interest rate were 1% greater, we can calculate the new interest earned using a rate of 9%. Then we subtract the original interest earned to find the difference:
New interest = $4,000 x 0.09 x 3 = $1,080
Difference = $1,080 - $960
Difference = $120
So Yvonne would have $120 more in her account if the interest rate were 1% greater.
To determine how much Yvonne has in her account at the end of 3 years, we need to add the original amount she deposited to the interest she earned. The formula for calculating simple interest is:
Interest = Principal * Rate * Time
Given that the interest earned is $960, the principal is $4,000, and the time is 3 years, we can rearrange the formula to solve for Rate:
Rate = Interest / (Principal * Time)
Plugging in the values:
Rate = $960 / ($4,000 * 3) = $960 / $12,000 = 0.08
The annual simple interest rate is 0.08 or 8%. Therefore, the account grew at a rate of 8% per year.
To calculate how much Yvonne would have in her account if the interest rate were 1% higher, we first need to find the new interest rate:
New Rate = Current Rate + 1% = 8% + 1% = 9%
Then we can calculate the interest she would earn with the new rate over 3 years:
New Interest = Principal * New Rate * Time = $4,000 * 9% * 3 = $1,080
Finally, we can add this new interest to the principal to find out how much Yvonne would have in her account:
New Account Balance = Principal + New Interest = $4,000 + $1,080 = $5,080
Therefore, if the interest rate were 1% greater, Yvonne would have $5,080 in her account at the end of 3 years.
To find out how much Yvonne has in her account at the end of 3 years, we can add the initial amount of $4,000 and the earned interest of $960.
The total amount in her account after 3 years is $4,000 + $960 = $4,960.
To calculate the annual simple interest rate, we can use the formula:
Interest = Principal * Rate * Time
$960 = $4,000 * Rate * 3
To find the rate, we can divide both sides of the equation by ($4,000 * 3):
$960 / ($4,000 * 3) = Rate
Rate = 0.08 or 8%
So, the annual simple interest rate is 8%.
To calculate how many more dollars Yvonne would have in her account if the interest rate were 1% greater, we need to find the new interest earned.
New Interest = Principal * Rate * Time
New Interest = $4,000 * (8% + 1%) * 3
New Interest = $4,000 * 9% * 3
New Interest = $360
Thus, Yvonne would have an additional $360 in her account if the interest rate were 1% greater.