You invest an amount of money at an annual simple interest rate of $6.25 \%$. You invest a second amount, $\$ 500$ less than the first, at an annual simple interest rate of $6 \%$. Let $x$ represent the amount invested at $6.25 \%$. Complete the following table.

	Principal, $P$	$\cdot$	Interest rate, $r$	$=$	Interest earned, $I$
Amount at $6.25\%$	$x$	$\cdot$	$\underline{\quad?\quad}$	$=$	$\underline{\quad?\quad}$
Amount at $6\%$	$\underline{\quad?\quad}$	$\cdot$	$\underline{\quad?\quad}$	$=$	$\underline{\quad?\quad}$

An investment of $P$ dollars increased to $A$ dollars in $t$ years. If interest was compounded continuously, find the interest rate.

$$A=4055, \quad P=1000, \quad t=20$$

An amount of $3000 was deposited in a bank at a rate of 2% annual interest compounded quarterly for 3 yr. The rate then increased to 3% annual interest and was compounded quarterly for the next 3 yr. If no money was withdrawn, what was the balance at the end of this time?

Suppose an investment account is opened with an initial deposit of $12,000 earning 7.2% interest compounded continuously. How much will the account be worth after 30 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. $250,000, original APR 3.95%, 2 points with a 0.25% discount per point.

Cheyenne Bennett earned $72 in simple interest in 9 months at an annual interest rate of 8%. How much money did she invest?

Maximum Profit Assume that the amount of money deposited in a bank is proportional to the square of the interest rate the bank pays on this money. Furthermore, the bank can reinvest this money at $12 \%$. Find the interest rate the bank should pay to maximize profit.

For the following exercise,

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

Solve the compound interest formula for the principal, $P$.

Figure $12.59$ is a contour diagram of the monthly payment on a $5$-year car loan as a function of the interest rate and the amount you borrow. The interest rate is $13 \%$ and you borrow $\$ 6000$ for a used car.

(a) What is your monthly payment?

At the beginning of the year, $\$ 3500$ was deposited in a savings account. One year later, $\$ 4000$ was deposited in another account. The interest rate was the same for both accounts. At the end of the second year, there was a total of $\$ 8518.35$ in the accounts. What was the annual interest rate?

Jessica invests $38,000; part at 7.5% simple interest and the remainder at 6% simple interest. If her annual interest income is$2600, how much does she have invested at each rate?

The final amount for $\$ 5000$ invested for $25$ years at $10 \%$ annual interest compounded semiannually is $\$ 57,337$. What is the effect of doubling the annual interest rate?

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.

For the following exercise, 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, $r$.