The unpaid balance of an installment loan is equal to the present value of the remaining payments. The unpaid balance, P, is given by $P=P M T \frac{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}{\left(\frac{r}{n}\right)}$, where PMT is the regular payment amount, r is the annual interest rate, n is the number of payments per year, and t is the number of years remaining in the loan. a. Use the loan payment formula to derive the unpaid balance formula. b. The price of a car is $24,000. You have saved 20% of the price as a down payment. After the down payment, the balance is financed with a 5-year loan at 9%. Determine the unpaid balance after three years. Round all calculations to the nearest dollar.

Write an original problem that can be solved using the Fundamental Counting Principle. Then solve the problem.

A credit card issuer calculates interest using the average daily balance method. The monthly interest rate is 1.1% of the average daily balance. The following transactions occurred during the November 1–November 30 billing period.

$$\begin{matrix} \text{Transaction Description} & \text{Transaction Amount}\\ \text{Previous balance, }{\$ \text 4620.80}\\ \text{November 1 Billing date}\\ \text{November 7 Payment} & \text{}{\$ \text 650.00 credit}\\ \text{November 11 Charge: Airline Tickets} & \text{}{\$ \text 350.25}\\ \text{November 25 Charge: Groceries} & \text{}{\$ \text 125.70}\\ \text{November 28 Charge: Gas} & \text{}{\$ \text 38.25}\\ \text{November 30 End of billing period}\\ \text{Payment Due Date: December 9}\\ \end{matrix}$$

a. Find the average daily balance for the billing period. Round to the nearest cent. b. Find the interest to be paid on December 1, the next billing date. Round to the nearest cent. c. Find the balance due on December 1. d. This credit card requires a $10 minimum monthly payment if the balance due at the end of the billing period is less than$360. Otherwise, the minimum monthly payment is $\frac{1}{36}$ of the balance due at the end of the billing period, rounded up to the nearest whole dollar. What is the minimum monthly payment due by December 9?

During the year, the following sales transactions occur. There is a charge of 3% on all credit card transactions and a 1%charge on all debit card transactions. Calculate the amount recorded as cash receipts from these transactions. 1. Total cash sales = $500,000 2. Total check sales=$350,000 3. Total credit card sales= $600,000 4. Total debit card sales =$200,000

A circle with a radius of 6 meters has an are that measures $35^{\circ}$. If this arc and its associated sector are completely removed from the circle, what is the length of the major are that remains, to the nearest tenth of a meter?

A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s$^2$ after its brakes are applied. What is the angular speed of the wheels when the car has traveled half the total distance?

Involve credit cards that calculate interest using the average daily balance method. The monthly interest rate is $1.2\%$ of the average daily balance. Each exercise shows transactions that occurred during the June $1$–June $30$ billing period. In each exercise,

a. Find the average daily balance for the billing period. Round to the nearest cent.

b. Find the interest to be paid on July $1$, the next billing date. Round to the nearest cent.

c. Find the balance due on July $1$.

d. This credit card requires a $\$30$ minimum monthly payment if the balance due at the end of the billing period is less than $\$400$. Otherwise, the minimum monthly payment is $\frac{1}{25}$ of the balance due at the end of the billing period, rounded up to the nearest whole dollar. What is the minimum monthly payment due by July $9$?

$$\begin{matrix} \text{Transaction Description} & \text{Transaction Amount}\\ \text{Previous balance, } & {\$ }\text{ 4037.93}\\ \text{June 1 Billing Date}\\ \text{June 5 Payment} & {\$ \text{ 350.00 credit}}\\ \text{June 10 Charge: Gas} & {\$ \text {31.17}}\\ \text{June 9 Charge: Prescriptions} & {\$ \text {42.50}}\\ \text{June 22 Charge: Gas Charge: Groceries} & {\$ \text{43.86} ~\$ \text{112.91}}\\ \text{June 29 Charge: Clothing} & {\$ \text{96.73}}\\ \text{June 30 End of billing period}\\ \text{Payment Due Date: July 9}\\ \end{matrix}$$

Write each expression as a single power of $x$. a. $(x^2)^6$ b. $(x^2)^5$ c. $(x^3)^9$ d. $(x^{10})^{10}$ e. $\dfrac{x^8}{x^2}$ f. $\dfrac{x^9}{x^7}$ g. $\dfrac{1}{x^6}(x^{14})$

Distinguish between an umbra and a penumbra?

Determine whether the polygons with the given vertices are similar. Support your answer by describing a transformation. A(3, 0), B(3, 6), C(9, 6), X(4, 0), Y(4, -8), Z(12, -8)

A man whose eye is 1.5 metres above ground level stands 20 metres from the base of a tree. The angle of elevation to the top of the tree is $45^{\circ}$. Calculate the height of the tree.

What is the purpose of a flagellum?

A parasail is attached by a 40-foot rope to the boat that is towing it. If the angle of elevation from the boat to the parasail is $34^{\circ}$, about how far above the water is the parasailer?

The unpaid balance of an installment loan is equa l to the present value of the remaining payments. The unpaid balance , P, is given by

$$P = P M T \frac { \left[ 1 - \left( 1 + \frac { r } { n } \right) ^ { - n t } \right] } { \left( \frac { r } { n } \right) }$$

where PMT is the regular payment amount , r is the annual interest rate , n is the number of payments per year, and t is the number of years remaining in the loan. a. Use the loan payment formula to derive the unpaid balance formula. b. The price of a car is $24,000. You have saved 20% of the price as a down payment. After the down payment, the balance is financed with a 5-year loan at 9%. Determine the unpaid balance after three years. Round all calculations to the nearest dollar.