Morgan charged 10000 on her credit card to relocate for her

Morgan charged $10,000 on her credit card to relocate for her first job. When she realized that the interest rate for the unpaid balance was 18% compounded monthly, she decided to not charge any more on that account. She wants to have this account paid off by the end of 3 years, so she arranges to have automatic payments sent at the end of each month. If there were no time period for which to pay off the debt, what is the smallest payment Morgan would have to make each month to never increase her debt? What monthly payment must she make to have the account paid off by the end of 3 years? How much total interest will she have paid if the loan is paid off in 3 years?

Solution

(a)The interest is $ 0.015*10000 = $ 150 for the 1st month if no repayment is made. Thus, if a repayment of $ 150 per month is made, the outstanding dues of $ 10000 will not change.

(b) The formula for ordinary annuity is p = r(PV)/ [ 1 – (1 +r)^-n ] where p is the monthly installment, r is the rate of interest in decimals and n is the number of months. Here, PV = 10000, r = 0.18/12= 0.015 and n = 3 * 12 = 36. Therefore, p= 0.015(10000)/ [( 1- ( 1+ 0.015)-³⁶ ] = 150/ [ 1 –0.585089735] = 150/ 0.414910264 = $ 361.52 . Thus, Morgan is required to make a payment of $ 361.52 per month to pay off the credit card dues in 3 years.

( c )In 3 years, the total amount paid is $ 361.52 * 36 = $ 13014.72. Thus, the interest paid in 3 years is $ 13014.72 - $ 10000 = $ 3014.72