PAYING OFF CREDIT CARDS

Simon recently received a credit card with an $14\%$ nominal interest rate. With the card, $1$ purchased an Apple iPhone $5$ for $$390.$ The minimum payment on the card is only $$10$ per month.

a$.$ If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest month.

$$ month$($s$)$

b$.$ If Simon makes monthly payments of $$30,$ how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest month. $$ month$($s$)$

c$.$ How much more in total payments will Simon make under the $$10-$a$-$month plan than under the $$30-$a$-$month plan. Do not round intermediate calculations. Round your answer to the nearest cent. $

EFFECTIVE VERSUS NOMINAL INTEREST RATES

Bank A pays $5\%$ interest compounded annually on deposits, while Bank $B$ pays $4\mathrm{.}5\%$ compounded daily.

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

I. You would choose Bank A because its EAR is higher.

II$.$ You would choose Bank $B$ because its EAR is higher.

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

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

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

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.

I. 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.

II$.$ 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.

III. 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.

IV$.$ 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.

V$.$ 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.