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?

A certain strain of bacteria divides every 3 hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by

$$t = 3 \frac { \log ( N / 50 ) } { \log 2 }$$

Find the time required for the colony to grow to a million bacteria.

How long will it take for an investment of $1000 to double in value if the interest rate is 8.5% per year, compounded continuously?

These exercises use the population growth model. A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. (a) What was the initial size of the bird population? (b) Estimate the bird population 5 years from now. (c) Sketch a graph of the bird population.

If $1000 is invested at 4% per annum compounded semiannually, how much is in the account after 2 years?

For the following exercises, 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

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.

Find the simple interest paid to the nearest cent for each loan amount, interest rate, and time. $725, 6.25%, 1 year

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

Explain what is wrong with the statement.

The present value of a lump-sum payment $S$ dollars one year from now is greater with an annual interest rate of $4\%$ than with an annual interest rate of $3\%.$

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?

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 learning curve is a graph of a function $P(t)$ that measures the performance of someone learning a skill as a function of the training time $t$. At first, the rate of learning is rapid. Then, as performance increases and approaches a maximal value $M$, the rate of learning decreases. It has been found that the function

$$P(t)=M-C e^{-k t}$$

where $k$ and $C$ are positive constants and $C<M$ is a reasonable model for learning.

(a) Express the learning time $t$ as a function of the performance level $P$.

(b) For a pole-vaulter in training, the learning curve is given by

$$P(t)=20-14 e^{-0.024 t}$$

where $P(t)$ is the height he is able to pole-vault after $t$ months. After how many months of training is he able to vault $12 \mathrm{ft}$ ?

(c) Draw a graph of the learning curve in part (b).

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%.