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

Suppose an amount P is invested at an interest rate r and A is the amount after t years.

(a) Write an expression for $A$ if the interest is compounded $n$ times per year.

(b) Write an expression for $A$ if the interest is compounded continuously.

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 = 7 %$

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.

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

The monthly payment on a $300,000 30 year mortgage at 6% annual interest rate is$1798.65. What is the interest payment for the first month?

Which of the following theoretical factors increases the rate of a reaction?

(a) increase collision frequency

(b) increase collision energy

(c) effective collision orientation

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 $T$.

Solve for the unknown interest rate in each of the following:

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.

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%$

Bill Rich signed a 180-day note for $1,250. He repaid the loan when due with interest at an annual rate of 12 % using a banker's year.

Tony Colito paid$19.50 in interest on a loan of $2,600 for 1 month. What rate of interest did he pay?

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%$

In $1975$, interest rates were $7.98 \%$ and the rate of inflation was $12.26 \%$ in the United States. What was the real interest rate in $1975$? How would the purchasing power of your savings have changed over the year?