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.

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

The Fort House Tea Room borrowed $17,500 for renovations at a simple interest rate of 6.85% for 4 years. The interest is to be paid annually. Find the amount of each annual interest payment.

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%

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

$10,000 bond with coupon rate 5.4% that matures in 12 years; current interest rate is 6.5%.

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%.

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

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?

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. $400,000, original APR 4.1%, 1 point with a 0.2% discount.

All rates of interest given here are annual rates. Calculate the rate of interest per year which will earn the given amount of interest: a) Principal $400 time 4 years interest$112, b) Principal $800 time 7 years interest$224

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?

To what sum will $2000 amount in eight years if invested at a 6% effective rate for the first four years and at 6% compounded semiannually thereafter?

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.

Jose must invest a total of $\$ 15,000$ in two accounts, one paying $4 \%$ simple annual interest, and the other paying $3 \%$. If he wants to earn $\$ 550$ annual interest, how much should he invest at each rate?