Future Value of an Annuity for Various Compounding Periods

Find the future values of the following ordinary annuities.

Payments of $$600$ every $6$ months for $7$ years at a nominal rate of $12\%,$ compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

$

Payments of $$300$ every $3$ months for $7$ years at a nominal rate of $12\%,$ compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

$

The annuities described in parts a and b have the same total amount of money paid into them during the $7-$year period, and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part a over the $7$ years. Why does this occur?

$-$Select$-$

The nominal deposits into the annuity in part $($b$)$ are greater than the nominal deposits into the annuity in part $($a$).$

The annuity in part $($a$)$ is compounded less frequently; therefore, more interest is earned on interest.

The annuity in part $($a$)$ is compounded more frequently; therefore, more interest is earned on interest.

The annuity in part $($b$)$ is compounded less frequently; therefore, more interest is earned on interest.

The annuity in part $($b$)$ is compounded more frequently; therefore, more interest is earned on interest.

$2)$ Effective versus Nominal Interest Rate

Universal Bank pays $11\%$ interest, compounded annually, on time deposits. Regional Bank pays $10\%$ interest, compounded quarterly.

Based on effective interest rates, in which bank would you prefer to deposit your money?

I. You would choose Regional Bank because its EAR $($or EFF$\%)$ is higher.

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

III. You would choose Universal Bank because its EAR $($or EFF$\%)$ is higher.

IV$.$ You would choose Regional Bank because its nominal interest rate is higher.

V$.$ You would choose Universal Bank because its nominal interest rate is higher.

$-$Select$-$ one of the following from $1-5$

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? In answering this question, assume that funds must be left on deposit during an entire compounding period in order for you to receive any interest.

I. If funds must be left on deposit until the end of the compounding period $(1$ year for Universal Bank and $3$ months for Regional Bank$),$ and you think there is a high probability that you will make a withdrawal during the year, then Regional Bank might be preferable.

II$.$ If funds must be left on deposit until the end of the compounding period $(3$ months for Universal Bank and $1$ year for Regional Bank$),$ and you think there is a high probability that you will make a withdrawal during the year, then Regional Bank might be preferable.

III. If funds must be left on deposit until the end of the compounding period $(1$ year for Universal Bank and $3$ months for Regional Bank$),$ and you have no intentions of making a withdrawal during the year, then Regional Bank might be preferable.

IV$.$ If funds must be left on deposit until the end of the compounding period $(1$ year for Universal Bank and $3$ months for Regional Bank$),$ and you think there is a high probability that you will make a withdrawal during the year, then Universal Bank might be preferable.

V$.$ If funds must be left on deposit until the end of the compounding period $(3$ months for Universal Bank and $1$ year for Regional Bank$),$ and you think there is a high probability that you will make a withdrawal during the year, then Universal Bank might be preferable.

$-$Select$-$ one of the following from $1-5$