A print shop borrows
$8400
from a credit union for
307
days. The credit union charges simple interest at an annual rate of
5.75%
for this loan. Assume each day is
1365
of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas
.
(a) Find the interest that will be owed after
307
days.
$
(b) Assuming the print shop doesn't make any payments, find the amount owed after
307
days.
$
(a) To find the interest that will be owed after 307 days, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Where the principal is $8400, the rate is 5.75% (or 0.0575), and the time is 307 days (or 307/365 of a year).
Interest = $8400 * 0.0575 * (307/365) ≈ $244.13
Therefore, the interest that will be owed after 307 days is approximately $244.13.
(b) To find the amount owed after 307 days, we need to add the interest to the principal:
Amount Owed = Principal + Interest
Amount Owed = $8400 + $244.13 ≈ $8644.13
Therefore, the amount owed after 307 days is approximately $8644.13.
This apparently is wrong. Both answers are wrong.
Apologies for the error. Let's recalculate the correct answers.
(a) To find the interest that will be owed after 307 days, we use the same formula as before:
Interest = Principal * Rate * Time
Interest = $8400 * 0.0575 * (307/365) ≈ $569.15
Therefore, the interest that will be owed after 307 days is approximately $569.15.
(b) To find the amount owed after 307 days, we add the interest to the principal:
Amount Owed = Principal + Interest
Amount Owed = $8400 + $569.15 ≈ $8969.15
Therefore, the amount owed after 307 days is approximately $8969.15.
Lena took out a loan for
1
month and was charged simple interest at an annual rate of
9.6%
.
The total interest she paid on the loan was
$112
.
How much money did Lena borrow?
Do not round any intermediate computations. If necessary, refer to the
list of financial formulas
.
$
Let x be the amount of money Lena borrowed.
To find the interest paid, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given that the total interest paid is $112 and the annual rate is 9.6%, we can write the equation as:
112 = x * 0.096 * (1/12)
Simplifying the equation, we get:
112 = x * 0.008
To solve for x, divide both sides of the equation by 0.008:
112/0.008 = x
x ≈ $14,000
Therefore, Lena borrowed approximately $14,000.
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with
205
grams of a radioactive isotope, how much will be left after
6
half-lives?
Use the calculator provided and round your answer to the nearest gram.
To find the amount of a radioactive isotope remaining after a certain number of half-lives, we can use the formula:
Final amount = Initial amount * (1/2)^(Number of half-lives)
Given that the initial amount is 205 grams and we want to find the amount remaining after 6 half-lives, we can substitute these values into the formula:
Final amount = 205 * (1/2)^(6)
Using a calculator, we can evaluate the expression:
Final amount ≈ 205 * (1/2)^6 ≈ 205 * 0.015625 ≈ 3.125
Therefore, approximately 3 grams of the radioactive isotope will be left after 6 half-lives.
interest, compounded monthly. Payments will be made at the end of each month.
How much money do they need to pay into the annuity each month for the annuity to have a total value of
$12,000
after
10
years?
Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the
list of financial formulas
.
$
To determine how much money the individual needs to pay into the annuity each month, we can use the formula for the future value of an annuity:
Future Value = Payment * [(1 + Rate)^Time - 1]/Rate
Given that the future value is $12,000, the time is 10 years, and the payments are made monthly, we can adjust the formula accordingly.
Future Value = Payment * [(1 + Rate/12)^(12*Time) - 1]/(Rate/12)
Substituting the known values, we have:
12,000 = Payment * [(1 + Rate/12)^(12*10) - 1]/(Rate/12)
To solve for the payment, we need to rearrange the formula:
Payment = Future Value * (Rate/12) / [(1 + Rate/12)^(12*Time) - 1]
Using this formula, we can compute the value of the payment:
Payment = $12,000 * (Rate/12) / [(1 + Rate/12)^(12*10) - 1]
Since the formula requires the interest rate, we need that information to provide an accurate answer.
The Turner family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns
5.4%
interest, compounded monthly. Payments will be made at the end of each month.
How much money do they need to pay into the annuity each month for the annuity to have a total value of
$12,000
after
10
years?
Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the
list of financial formulas
.
$