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 -$6000

B -$6048

C -$6100

D -$6150

E -$6200

ANSWER IS ACAN SOMEONE PLEASE EXPLAIN?

Hmmmmm. What does "10% return on purchase" mean? 10% return for the first year? If so, you could set it up as follows:

Let x=purchase price

1.1x=price after one year

1.05*1.1x=price after second year

1.05*1.1x-500=price after early redemption penalty.

1.05*1.1x-500=6430

Solve for x=6000.

So that gives you the right answer. But again, I'm not sure how to interpret "10% return on purchase" when they don't specify a timeframe. Maybe someone else with more of an investment background can chime in.

What's the source on this anyway? Seems a little calculation-heavy for a GMAT problem.

Thanks again for your help!! I found this question on the grockit website...wording seemed very weird to me as well

GmatMathPro wrote:
What's the source on this anyway? Seems a little calculation-heavy for a GMAT problem.

I agree with you. Normally you don't expect/encounter such calculation based problem in GMAT.

10% flat meams a 10% return in the 1st yr it self...question states "offers a 10% return on purchase"..compound interest starts from 2nd yr...

@Pete
How are we assuming that the compounding of interest is based on the new principal amount of 1.1x? Is there something in problem that allows us to assume that? Hope you can clarify... I thought it would be
0.1x (Purchase return)
x (original principal)
0.055x (compounded interest accrued....based on principal balance of x and not 1.1x)

Plz clarify...Thanks

factor26 wrote: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 -$6000

B -$6048

C -$6100

D -$6150

E -$6200

ANSWER IS ACAN SOMEONE PLEASE EXPLAIN?

We can plug in the answers, which represent the amount invested.
In problems involving COMPOUND interest, the initial investment is almost always a very "round" number.
Thus, the OA is likely to be A.

Answer choice A: 6000
Amount at the end of the first year = 600 + .1(600) = 6600.
Amount at the end of the second year = 6600 + .05(6600) = 6930.
Amount after the early redemption penalty = 6930-500 = 6430.
Success!

The correct answer is A.

I worked backwards which I found easier for me:

You start with 6430. The last thing the problem says is there is a $500 penalty. So you add 500:

6340 + 500 = 6930.

The second last thing stated in the problem is 5% was added. Consequently subtract by 5%.

6930 - .05(6930) = 6930 - 350(approximately) = 6580.

The first thing the problem says is to add 10% so the last step working backwards would be to subtract by 10%.

6580 - .10(6580) = 6580 - 658 = 5922

The reason we end up with 5922 is because we rounded higher in the second step thus making the final result smaller. As you can see from the answer choices 6000 is the closest answer so the answer is A.

sk8legend408 wrote:I worked backwards which I found easier for me:

You start with 6430. The last thing the problem says is there is a $500 penalty. So you add 500:

6340 + 500 = 6930.

The second last thing stated in the problem is 5% was added. Consequently subtract by 5%.

6930 - .05(6930) = 6930 - 350(approximately) = 6580.

The first thing the problem says is to add 10% so the last step working backwards would be to subtract by 10%.

6580 - .10(6580) = 6580 - 658 = 5922

The reason we end up with 5922 is because we rounded higher in the second step thus making the final result smaller. As you can see from the answer choices 6000 is the closest answer so the answer is A.

I believe one of the reasons you ended up with 5922 is because there's a flaw in your approach.

Let me illustrate:

If X+0.05X=A,

We cannot go from A to X by subtracting 0.05A from A. To go from A to X, we need to subtract 0.05X. But, we don't know what X is in advance. Your answer was not too far off because X in this case was close enough to A that your method yielded a number that was close to the answer.

kakz wrote:@Pete
How are we assuming that the compounding of interest is based on the new principal amount of 1.1x? Is there something in problem that allows us to assume that? Hope you can clarify... I thought it would be
0.1x (Purchase return)
x (original principal)
0.055x (compounded interest accrued....based on principal balance of x and not 1.1x)

Plz clarify...Thanks

Compound interest will be calculated based on the principal + any interest or accrued amount in the account. You can think of the note as a bank savings account. Any money you or someone else puts into that account is eligible for the same rate of interest as the principal amount that was deposited into the account.