The following pairs of investment plans are identical except for a small difference in interest rates. Compute the balance in the accounts after $10$ and $30$ years. Discuss the difference.

Jose invests $\$ 1500$ in an account that earns $5.6 \%$ compounded annually. Marta invests $\$ 1500$ in a different account that earns $5.7 \%$ compounded annually.

Use the formula for continuous compounding to compute the balance in account after $1$, $5$, and $20$ years. Also, find the APY for below account. A $\$ 3000$ deposit in an account with an APR of $7.5 \%$

How much must you deposit today into the following accounts in order to have $\$ 25,000$ in $8$ years for a down payment on a house? Suppose that no additional deposits are made. An account with daily compounding and an APR of $4 \%$

Find the annual percentage yield (to the nearest $0.01 \%$ ) in below case. A bank offers an APR of $3.2 \%$ compounded monthly.

If the basic relationships in previous section. 1 hold, then what will be the relationship between the expected change in the Ruritanian/dollar exchange rate and the interest rates in the United State and Ruritania? Suppose that you were confident that the exchange rate would not change over the coming year. Does this open up a profit opportunity?

Use the appropriate compound interest formula to compute the balance in account after the stated period of time. $\$ 10,000$ is invested for $5$ years with an APR of $2.75 \%$ and monthly compounding.

By using the compound interest formula to compute the balance in account after the stated period of time, assuming that interest is compounded annually. $\$ 3000$ is invested at an APR of $1.8 \%$ for $12$ years.

Estimate the amount of money you will have in account after $5$ years, assuming that the account earns simple interest. You deposit $\$ 1800$ in an account with an annual interest rate of $3.8 \%$

Decide whether the following statement is true or false. Explain your reasoning. No bank could afford to pay interest every trillionth of a second because, with compounding, it would soon owe everyone infinite dollars.

What is continuous compounding? How does the APY for continuous compounding compare to the APY for, say, daily compounding? Explain the formula for continuous compounding.

Use the formula for continuous compounding to compute the balance in the following accounts after $1$, $5$, and $20$ years. Also, find the $\mathrm{APY}$ for each account.

A $\$ 3000$ deposit in an account with an $\mathrm{APR}$ of $7.5 \%$

Use the formula for continuous compounding to compute the balance in the following accounts after $1$, $5$, and $20$ years. Also, find the $\mathrm{APY}$ for each account.

A $\$ 500$ deposit in an account with an $\mathrm{APR}$ of $2.7 \%$

Use the formula for continuous compounding to compute the balance in the following accounts after $1$, $5$, and $20$ years. Also, find the $\mathrm{APY}$ for each account.

A $\$ 3000$ deposit in an account with an $\mathrm{APR}$ of $6 \%$

Use the formula for continuous compounding to compute the balance in the following accounts after $1$, $5$, and $20$ years. Also, find the $\mathrm{APY}$ for each account.

A $\$ 7000$ deposit in an account with an $\mathrm{APR}$ of $4.5 \%$