The interest rate on a car loan affects the monthly payment. The function that relates the monthly payment for a 5 -year loan (60-month loan) to the monthly interest rate is given by

$$P(x)=\frac{C x}{\left[1-\frac{1}{(x+1)^{60}}\right]}$$

where $x$ is the monthly interest rate (as a decimal), $C$ is the loan amount, and $P(x)$ is the monthly payment.

Simplify the complex fraction.

True or False? If true, prove it. If false, find the true answer. If you invest $500, an annual rate of interest of 3% yields more money in the first year than a 2.5% continuous rate of interest.

Find the simple interest paid to the nearest cent for each loan amount, interest rate, and time. $1,000, 7%, 2 years

For the following exercise, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.

Deposit amount: $\$ 100$; total deposits: 120 ; interest rate: $10 \%$, compounded semi-annually

To what sum will $2000 amount in eight years if invested at a 6% effective rate for the first four years and at 6% compounded semiannually thereafter?

Suppose that $10,000 is invested at continuous rate r and grows to$17,160 in 9 years. Find the interest rate r.

A $4000 certificate of deposit is purchased for$4000 and is held for eleven years. If the certificate earns an effective rate of 7%, what is it worth at the end of that period?

Find the compound amount and compound interest if $4000 is invested for six years and interest is compounded continuously at the given annual rate. 9%

A loan of $\$ 10,000$ was repaid at the end of $6$ months. What amount (principal and interest) was repaid, if a $6.5 \%$ annual rate of interest was charged?

On May 15, Criqui Outback Clothiers borrowed some money on a 4-month note to provide cash during the slow season of the year. The interest rate on the note was 8%. At the time the note was due, the amount of interest owed was $480.

Instructions

(b) Assume the amount borrowed was$18,500. What was the interest rate if the amount of interest owed was $555?

A couple decides to accept an adjustable rate, 30-year mortgage, in which the interest rate is fixed for the first 5 years and then may be adjusted annually beginning with year 6. Suppose that this couple borrows $305,000 with the annual interest rate, compounded monthly, for the first 5 years set at 5.5%. Suppose that the interest rate is increased to 6.75% for the remaining term of the loan. Calculate the monthly payment during the first 5 years and after the first 5 years. Find the amount of interest that would be paid over the term of this loan

A company issued bonds with a $100,000 face value, a 5-year term, a stated rate of 6%, and a market rate of 7%. Interest is paid annually. What is the amount of interest the bondholders will receive at the end of the year?

You are investing P dollars at an annual interest rate of r, compounded continuously, for t years. Which of the following would result in the highest value of the investment? Explain your reasoning. Double your interest rate.

Find the time required for a $1000 investment to (a) double at interest rate r, compounded continuously, and (b) triple at interest rate r, compounded continuously. Round your results to two decimal places.$r = 2.5%$