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.

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?

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.

$25,000 bond with coupon rate 7% that matures in 10 years; current interest rate is 6%.

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?

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

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

$15,000 bond with coupon rate 6% that matures in 4 years; current interest rate is 5%.

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.

A $4000 certificate of deposit is purchased for$4000 and is held for eleven years. If the certificate earns an effective rate of 7%, what is it worth at the end of that period?

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?

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

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

(a) increase collision frequency

(b) increase collision energy

(c) effective collision orientation

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%.

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