The formula

$$I_t=\frac{I_f}{1-T}$$

gives the taxable interest rate $I_t$ equivalent to the tax-free interest rate $I_f$ for a person in the $(100 \cdot T) \%$ tax bracket. Solve for $T$.

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%$

Find the monthly payment, amount paid, and interest charged for a $90,000 mortgage loan at an annual interest rate of 10% for 20 years.

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.

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?

In this exercise, use the add-on method of calculating interest to find the total interest and the monthly payment.

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 = 3.75%$

If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed as a decimal, the interest I charged is _______ = _______. Interest charged according to this formula is called ________ _________.

In this exercise, use the add-on method of calculating interest to find the total interest and the monthly payment.

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 = 6%$

Find the monthly interest rate $r$ when

$$A P R=13.2$$

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

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