The monthly payment that amortizes a loan of A dollars in t years when the interest rate is r/year compounded monthly, is given by $P=f(A, r, t)=\frac{A r}{12\left[1-\left(1+\frac{r}{12}\right)^{-12 t}\right]}$ a. What is the monthly payment for a home mortgage of $300,000 that will be amortized over 30 years with an interest rate of 4%/year? An interest rate of 6%/year? b. Find the monthly payment for a home mortgage of$300,000 that will be amortized over 20 years with an interest rate of 6%/year.

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 number of years it would take for $1200 to earn simple interest of$324 at an annual interest rate of 6% per year.

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%

Find the price a purchaser should be willing to pay for the given bond. Assume that the coupon interest is paid twice a year.

$20,000 bond with coupon rate 4.5% that matures in 8 years; current interest rate is 5.9%.

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

(a) increase collision frequency

(b) increase collision energy

(c) effective collision orientation

A sum of $1000 was invested for 4 years, and the interest was compounded semiannually. If this sum amounted to$1435.77 in the given time, what was the interest rate?

Suppose that $20,000 is invested at continuous rate r and grows to$81,104 in 28 years. Find the interest rate r.

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

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?

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?

Assume federal debt reaches about $\$ 20$ trillion in $2017$.

If interest rates remain at the $2012$ level of $2.1 \%$, find the interest payment on the debt. Discuss the change in the interest payment with a $0.5$-point increase in the interest rate.

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 = 3.75%$