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 %$

Work the following applied problem.

Which of these 20-year zero-coupon bonds will be worth more at maturity: one that sells for $4510, with a 6.1% interest rate, or one that sells for$5809, with a 4.8% interest rate?

The bank offered a 0.6% interest rate. Find 0.6% of $1300.

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.

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?

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

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.

What happens to the present value of an annuity as the interest rate increases?

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?

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 make CDs look more attractive than they really are, some banks advertise that their rates are higher than their competitors’ rates; however, the fine print says that the rate is a simple interest rate. If a person deposits $10,000 at 10% per year simple interest, what compound interest rate would yield the same amount of money in 3 years?

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?

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 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.