Question

Kyle purchased a new TV and a DVD player on September 1, 2019, for $1,500 and used her father's credit card to pay for it. His father agreed to allow Kyle to use the card based on her paying the balance within one year. The nominal interest rate on the card is 24% compounded monthly and requires equal monthly payments. The first payment was on October 1, 2019.After six months of paying for these purchases, Kyle decided, on March 1, 2020, that she also could purchase a stereo for $1,000. Kyle's father still insisted that Kyle pay the total balance within one year from the date of the first purchase. Assume that the new purchase is to be immediately applied to the unpaid balance and Kyle made the payment due at the beginning of March before purchasing the stereo. What is the amount of the payments for the first six months and the amount of the payments for the second six months?

Answer 1

Kyle purchased TV and DVD playeron Sept 1, 2019 for $1,500

Rate of Interest (r) = 24% per year compounded monthly which is 24% / 12 = 2% per month

Monthly EMI can be calculated as: {[Loan Amount * r * (1 + r)^^{Months for which loan is taken}] / [(1 + r^^{Months for which loan is taken} - 1]}

EMI for TV and DVD would be: {[1,500 * 0.02 * (1 + 0.02)¹²] / [(1 + 0.02)¹² - 1]} = $141.83

She paid this $141.83 for six months and she purchased a stereo for $1,000 on 1 March, 2020.

EMI of stereo would be: {[1,000 * 0.02 * (1 + 0.02)⁶] / [(1 + 0.02)⁶ - 1]} = $178.52

Kyle is paying EMI of TV and DVD for first 6 months which means she is paying $141.83 per month while after six months she is paying EMI of stereo as well which make monthly payment equal to $141.83 + $178.52 = $320.35