Problem Solving

A 5-year investment note offers a 10% return on purchase, and a compounding 5% for each year after the first. If there is a $500 penalty for early redemption, and the note is redeemed for $6430 after the second year, what was the original purchase price?

A. $ 6,000
B. $ 6,048
C. $ 6,100
D. $ 6,150
E. $ 6,200

I don't understand when the question says: "A 5-year investment note offers a 10% return on purchase". Here, I think that the note pays the 10% at the end of the five years. So, if the note is sold in the second year, the interest will be Capital*0.10*(2 years / 5 years).
In addition, the phrase "a compounding 5% for each year after the first" doesn't indicate that that amount will be calculated after the capitalization of the original 10%.
I say this because, according to the OE, this is the solution:

P*1.1*1.05 - 500 = 6430
P is the original Price.

IMO, this question is not good at all. What do you think? Do you expect something like this in the real GMAT? Does it worth the time of studying it? Thanks!

OA is A.

Let the original investment is x....(1)

During purchase we get 10% return which equals 0.1*x....(2)

Compound Interest starts from second year(and a compounding 5% for each year after the first), so Compound Interest from start of second year to the end of second year equals (x(1+5/100) - x)....(3)

$500 is the penalty for early redemption which is in second year.

So final equation becomes x + 0.1*x + (x(1+5/100) - x) - 500 = 6430.

Solving we get x = 6026(approx)

Answer A.

What is the source?

It does not look like a real GMAT question, moreover options are really close.

Thanks
Puneet

Check my posts here:

https://www.beatthegmat.com/ps-percentag ... 07244.html

Let Principal = p
Principal after 1st year= 1.1p (Ten percent return on investment)

Since the amount is being withdrawn after 2nd year. There will be a penalty of 500

For 2nd year return :
6430 = 1.1p (1+5/100)^1 - 500
p = $ 6000

OA is A