Use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.

Use properties of rational exponents to solve the compound interest formula for the interest rate, $r$.

Suppose you deposit in dollars at the beginning of every month in a savings account that earns a monthly interest rate of r, which is the annual interest rate divided by 12 (for example, if the annual interest rate is 2.4%, r=0.024 / 12=0.002). For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest, or m+m(1+r). Continuing in this fashion, it can be shown that the amount of money in your account after n months is $A_{n}=m+m(1+r)+\cdots+m(1+r)^{n-1}$. Use geometric sums to determine the amount of money in your savings account after 5 years (60 months) using the given monthly deposit and interest rate. Monthly deposits of $100 at an annual interest rate of 1.8%

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?

At bank A, $600 is invested with an interest rate of 5% compounded annually. At bank B,$500 is invested with an interest rate of 6% compounded quarterly. Which account will have a larger balance after 10 years? 20 years

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 $1$-point increase in the interest rate.

In years 1 and 2, the consumer price index is 125 and 160, respectively. Every inflation is expected. What is the real interest rate at Commerce Bank of Beverly Hills if year two's interest rate is 35 percent?

For the following exercises, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}.$ Use properties of rational exponents to solve the compound interest formula for the interest rate, r.

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?

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.

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%.

Determine the cost of the points and the new interest rate for each loan amount and interest rate. Assume each point costs 1% of the loan amount. $550,000, original APR 4.75%, 1 point with a 0.3% discount.

Suppose you deposit in dollars at the beginning of every month in a savings account that earns a monthly interest rate of r which is the annual interest rate divided by 12 (for example, if the annual interest rate is 2.4%, r=0.024 /12=0.002). For an initial investment of m dollars, the amount of money the your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest, or m + m(1 + r). Continuing this fashion, it can be shown that the amount of money in your account after n months is $A_{n}=m+m(1+r)+\cdots+m(1+r)^{n-1}$. Use geometric sums to determine the amount of money in your savings account after 5 years (60 months) using the given monthly deposit and interest rate. Monthly deposits of $250 at a monthly interest rate of 0.2%.

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.

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.

Kelly Bullock borrowed$4,800 for 6 months and paid $264 interest. What rate of interest did she pay?