Calculate each scenario. You have $1,500 in credit card debt on several cards, e

Question

Calculate each scenario. You have $1,500 in credit card debt on several cards, each of which has an outrageously high interest rate. You want to consolidate your debt and formulate a plan to pay it off in one year, so you are comparing two credit card offers. Card A offers an APR of 18.6% while Card B offers no interest for the first six months and then an APR of 20.5% after that. If you transfer the balance of $ 1,500 to Card A, find how much you will need to pay each month in order to pay off the whole balance in one year. Suppose you pay the amount computed in part (a) of this Exploration but under the scenario offered by Card B. That is, you pay that amount each month, but for the first six months, no interest is being charged, so you are reducing your principal. How much would you need to pay each month for the final six months of the year to play off the remaining balance on Card B by the end of the year? How much interest would you pay under each of the plans?

Explanation / Answer

Formula for calculating the instalment is:

Payment = (r * PV) / [1-(1+r)^(-n)]

where,

PV is the Present value

r = rate per period

n = number of periods

(a) Here PV = $1500, r = 18.6%/12 and n = 12

Applying the above formula we get

Instalment payment = ((18.6%/12)*1500)/(1-((1+18.6%/12)^(-12))) = $137.95

[Note: the same could be found out by using the PMT formula of excel as follows:

PMT(18.6%/12,12,-1500) = $137.95 ]

(b)

Principal payment for the first 6 months = $137.95 x 6 = $827.70

Balance principal to be repaid in the next 6 months at 20.5% APR = $1500 - $827.70 = $672.30

The required instalment

= ((20.5%/12)*672.3)/(1-((1+20.5%/12)^(-6)))

= $118.84

[using excel, PMT(20.5%/12,6,-672.3) = $118.84]

For each of the last 6 months the amount required to be paid = $118.84

(c)

The interest paid under plan (a) = 12 x $137.95 - $1500 = $155.40

Ther interest paid under plan (b) = $137.95 x 6 + $118.84 x 6 - $1500 = $40.74

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