$1.$How long will it take $$200$ to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places.

$7\%.$

year$($s$)$

$10\%.$

year$($s$)$

$21\%.$

year$($s$)$

$100\%.$

year$($s$)$

$5.$You borrow $$165,000$; the annual loan payments are $$17,503\mathrm{.}08$ for $30$ years. What interest rate are you being charged? Round your answer to the nearest whole number.

$\%$

$7.$eBook Problem Walk$-$Through

Your client is $39$ years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $$7,000$ per year, and you advise her to invest it in the stock market, which you expect to provide an average return of $12\%$ in the future.

If she follows your advice, how much money will she have at $65?$ Do not round intermediate calculations. Round your answer to the nearest cent.

$

How much will she have at $70?$ Do not round intermediate calculations. Round your answer to the nearest cent.

$

She expects to live for $20$ years if she retires at $65$ and for $15$ years if she retires at $70.$ If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Do not round intermediate calculations. Round your answers to the nearest cent.

Annual withdrawals if she retires at $65$: $

Annual withdrawals if she retires at $70$: $

$10.$eBook Problem Walk$-$Through

Find the future values of the following ordinary annuities:

FV of $$500$ paid each $6$ months for $5$ years at a nominal rate of $15\%$ compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

$

FV of $$250$ paid each $3$ months for $5$ years at a nominal rate of $15\%$ compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

$

These annuities receive the same amount of cash during the $5-$year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a$.$ Why does this occur?

$-$Select$-$

$12.$ eBook

Bank A pays $6\%$ interest compounded annually on deposits, while Bank B pays $5\mathrm{.}25\%$ compounded daily.

a$.$ Based on the EAR $($or EFF$\%),$ which bank should you use?

You would choose Bank A because its EAR is higher.

You would choose Bank B because its EAR is higher.

You would choose Bank A because its nominal interest rate is higher.

You would choose Bank B because its nominal interest rate is higher.

You are indifferent between the banks and your decision will be based upon which one offers you a gift for opening an account.

$-$Select$-$

b$.$ Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest.

If funds must be left on deposit until the end of the compounding period $(1$ year for Bank A and $1$ day for Bank B$),$ and you think there is a high probability that you will make a withdrawal during the year, then Bank A might be preferable.

If funds must be left on deposit until the end of the compounding period $(1$ year for Bank A and $1$ day for Bank B$),$ and you have no intentions of making a withdrawal during the year, then Bank B might be preferable.

If funds must be left on deposit until the end of the compounding period $(1$ day for Bank A and $1$ year for Bank B$),$ and you think there is a high probability that you will make a withdrawal during the year, then Bank B might be preferable.

If funds must be left on deposit until the end of the compounding period $(1$ year for Bank A and $1$ day for Bank B$),$ and you think there is a high probability that you will make a withdrawal during the year, then Bank B might be preferable.

If funds must be left on deposit until the end of the compounding period $(1$ day for Bank A and $1$ year for Bank B$),$ and you think there is a high probability that you will make a withdrawal during the year, then Bank A might be preferable.

$-$Select$-$