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Need expert thought (% problem)

by voodoo_child » Sat Oct 08, 2011 4:57 am
Two payment schemes are available for customers in the N'K store. The first scheme includes a downpayment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a downpayment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

(A) 14%
(B) 27%
(C) 30%
(D) 34%
(E) 35%

I could get the OA C) by assuming that the down payment doesn't subtract the capital cost (or purchase price). If we do, the answer would be different. Can anyone please explain?

Here's what i am talking about:

scheme 1:

down payment = $43.20
remaining payment = 216-43.20 = 172.80
10% of this is $17.28
10 months of this payment is 172.80
total payment = 43.20+172.80 = 216 {Alternatively, one can also solve the equation to derive the result that total payment = purchase price!}

scheme 2

down payment = $21.60
remaining payment = 216-21.60 = 194.40
8% of this is $15.52
20 months of this payment is 311.04
total payment = 21.60+311.01 = 332.64

% less => (332.64-216)/332.64 = 35%

Any thoughts please?

maybe i didnt understand the question properly
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by shankar.ashwin » Sat Oct 08, 2011 5:34 am
Scheme 1

10% * 10 months = 100% = 216 (Org Cost)

Initial Payment = (20/100) * 216 = 43.2

Total = 259.2

Scheme 2

8% * 20 months = 160% = 1.6*216 = 345.6

Initial Payment = 10% = 21.6

Total = 367.2

Difference %= (367.2-259.2)/367.2*100 = [spoiler]30%[/spoiler] (approx)

P.S (I am guessing everything is compared to Original Cost)

We could directly do,

Scheme 1 - We pay 120% of total and Scheme 2 we pay 170%

So (170-120)/170 * 100 = 30% (Approx)
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by sl750 » Sat Oct 08, 2011 5:42 am
voodoo_child wrote:Two payment schemes are available for customers in the N'K store. The first scheme includes a downpayment of 20% of the purchase price and 10 monthly payments of 10% each. The second includes a downpayment of 10% and 20 monthly payments of 8% each. If a customer buys a TV for $216, by what percent will he find the first scheme cheaper than the second (approximately)?

(A) 14%
(B) 27%
(C) 30%
(D) 34%
(E) 35%

I could get the OA C) by assuming that the down payment doesn't subtract the capital cost (or purchase price). If we do, the answer would be different. Can anyone please explain?

Here's what i am talking about:

scheme 1:

down payment = $43.20
remaining payment = 216-43.20 = 172.80
10% of this is $17.28
10 months of this payment is 172.80
total payment = 43.20+172.80 = 216 {Alternatively, one can also solve the equation to derive the result that total payment = purchase price!}

scheme 2

down payment = $21.60
remaining payment = 216-21.60 = 194.40
8% of this is $15.52
20 months of this payment is 311.04
total payment = 21.60+311.01 = 332.64

% less => (332.64-216)/332.64 = 35%

Any thoughts please?

maybe i didnt understand the question properly
If I understood you correctly, it is normal practice to make the down payment first and the balance amount is paid in monthly installments of whatever the interest is being charged. Your reasoning is correct here
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