Question

. You have a $28,000 balance on your credit card. You plan to make monthly payments of $550 until the balance is paid off. The interest rate on your credit card is 19.5% p.a., compounded monthly. A letter in the mail informs you that you are approved for a new credit card and balance transfers are subject to a 8.5% p.a., compounded monthly. How many months sooner will you pay off your bill?

Answer 1

When i = 19.5%,

EMI = P*i*[(1+i)^n]/[{(1+i)^n}-1]

Where,

EMI = 550

P = Principal = $28000

i= Interest Rate = 0.195/12 = 0.01625

n= Number of periods

Therefore,

550 = 28000*0.01625*(1+0.01625)^n/[{(1+0.01625)^n}-1]

550 = 455*(1+0.01625)^n/[{(1+0.01625)^n}-1]

1.20879 = (1+0.01625)^n/[{(1+0.01625)^n}-1]

By Trial & Error,

Taking n = 100, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 1.24922

Taking n = 105, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 1.22557

Taking n = 108, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 1.21266

Taking n = 110, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 1.20453

Taking n = 109, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 1.20855

Therefore, 109 payments

When i = 8.5%

EMI = P*i*[(1+i)^n]/[{(1+i)^n}-1]

Where,

EMI = 550

P = Principal = $28000

i= Interest Rate = 0.085/12 = 0.007083

n= Number of periods

Therefore,

550 = 28000*0.007083*(1+0.007083)^n/[{(1+0.07083)^n}-1]

550 = 198.33*(1+0.007083)^n/[{(1+0.007083)^n}-1]

2.773 = (1+0.01625)^n/[{(1+0.01625)^n}-1]

By Trial & Error,

Taking n = 25, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 3.01497

Taking n = 30, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 2.608

Taking n = 27, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 2.834

Taking n = 28, (1+0.01625)^n/[{(1+0.01625)^n}-1] = 2.753

Therefore, 28 payments

Number of months, the bill will be paid sooner = 109-28 = 81 months sooner