1.) an account invested in a month market fund grew from $67,081.20 to $67,359.39 in a month. What was the interest rate, to the nearest tenth?
2.)you are due a tax refund of $760. your tax preparer offers you a no-interest loan to be repaid by your refund check, which will arrive in four weeks. she charges a $60 fee for this service. what actual interest rate will you pay for this loan?
3.)Let y base 1 be the future value after t years of $100 invested at 8% annual simple interest. let y base 2 be the future value after t years of $200 invested at 3% annual simple interest.
a.) think of y base 1 and y base 2 as functions of t and write the rules of these functions.
b.) without graphing, describe the graphs of y base 1 and y base 2.
YOu are going to have to show some work or thought on these. WE are not going to do your homework for you. What is it about these you don't understand. All are simple formulas.
1.) To find the interest rate, we can use the formula:
Interest = Final Amount - Initial Amount
In this case, the initial amount is $67,081.20 and the final amount is $67,359.39. So,
Interest = $67,359.39 - $67,081.20 = $278.19
Now, we can calculate the interest rate using the formula:
Interest Rate = (Interest / Initial Amount) * 100
Interest Rate = ($278.19 / $67,081.20) * 100 = 0.4149% (rounded to the nearest tenth)
Therefore, the interest rate, to the nearest tenth, is approximately 0.4%.
2.) To calculate the actual interest rate for the loan, we need to consider the fee charged for the service. The total amount you will have to repay is the loan amount ($760) plus the fee ($60), which is $820.
Now, we can calculate the actual interest rate using the following formula:
Interest Rate = ((Total Repayment - Loan Amount) / Loan Amount) * (100 / Time)
Here, the total repayment is $820 (loan amount + fee), the loan amount is $760, and the time is four weeks.
Interest Rate = (($820 - $760) / $760) * (100 / (4/52)) = 13.1579%
Therefore, the actual interest rate you will pay for this loan is approximately 13.2%.
3.) a.) The future values, y base 1 and y base 2, can be written as functions of t as follows:
For y base 1:
y base 1(t) = $100 + ($100 * 8% * t)
For y base 2:
y base 2(t) = $200 + ($200 * 3% * t)
In these formulas, t represents the number of years, and the percentages are converted to decimal form (8% = 0.08, 3% = 0.03).
b.) Without graphing, we can describe the graphs of y base 1 and y base 2 as follows:
The graph of y base 1 will be a straight line with a positive slope because the future value increases linearly with time due to simple interest. The initial value is $100, and it increases by 8% of the initial amount every year.
The graph of y base 2 will also be a straight line, but with a lower slope. This is because the future value increases at a slower rate compared to y base 1. The initial value is $200, and it increases by 3% of the initial amount every year.