Mac?s.cedit card situation is out of conrel bscause.sbe cannot afford to make he

Question

Mac?s.cedit card situation is out of conrel bscause.sbe cannot afford to make her monthly paxnents. She has three credit cards with the following kanbalances and APRs: Card 1, S4.500, 21%; Card 2, ss,700, 24%; ed.an 3, s3,200, 18%. Interest cemeounds mootbly. on all loan balances. A credit catd loan consolidation company has captured Mary's ateosen by stating they can save Mary 25% per month eo her credit card payments. This company charges 16.5% APR is the company's dam correct? a. If you are told that your effective annual interest tate. 10%, what is the nominal interest rate sempounded quarterly? .What is the effective annual interest rate if the nominal interest rate is 7%, and the frequency of s90RRuosing is once a month? C. How much time would it take for your principal to a gruRl,if the effective annual interest rate is 5%, and the frequency of compounding is once a year?

Explanation / Answer

Mary credit card...

A(card 1) = $4,500 (A/P, 21/12%, 120) = $89.97

A(card 2) = $5,700 (A/P , 24/12%, 120) = $125.67

A(card 3) = $3,200 (A/P, 1.5%, 120) = $57.66

A(consolidated) = $13,400 ( A/P, 16.5/12%, 120) = $228.66

Mary's current monthly payment is $273.30.

The consolidated payment represents

(273.30 - 228.66)/273.30 *100 = 16.3%

So while consolidating the credit cards, will benefit Mary, the company overstate the amount of this savings.

A) The formula for Effective interest rate(i):

i = (1+ r/t)t - 1

where,

r = nominal interest rate

t = compounded period.

i = effective interest rate.

Put values in the formula, we get

0.1 = (1 + r/4)4 -1

1.1 = (1+r/4)4

(1.1)0.25 = 1+r/4

1.024 -1 = r/4

r = 0.09645 so nominal interest rate anuualy.

Nominal interest rate compounded quarterly = 0.09645/4 = 0.024 = 2.4%

B) Again put values in the formula, we get

i = (1 + 0.07/12)12 -1

i = 0.07229

So effective annual interest rate = 7.23%

C) quadruple = 4 times

$4 = $1* (1+0.05)t

t represent time .

$4 = 1.05t

log 4 = t* log 1.05

t = 28.41 years.

So it take 28.41 years to quadruple your principle.

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