An investment of $200,000 in an instrument that returns an annual rate

Question

An investment of $200,000 in an instrument that returns an annual rate of r percent compounded semi-annually grows to $220,500 in one year. What is the value of r?

A. 5%
B. 5.125%
C. 10%
D. 10.25%
E. 20%

Chethan92 · Answer

CI =  P* r/2 ]^2 
P = 200,000
r = rate of interest
2 = Compounded semi-annually.

220500 = 200000 ^2
220500/200000 =  ^2
441/400 =  ^2
1+r/2 = 21/20
2+r = 2.1
r = 0.1

r = 10% interest.

C is the answer.

ScottTargetTestPrep · Answer

Solution:

We can use the compound interest formula A = P(1 + r/n)^(nt) to solve this problem. Here, A = 220,500, P = 200,000, n = 2, and t = 1, and we need to solve for r:

220,500 = 200,000(1 + r/2)^(2 x 1)

1.1025 = (1 + r/2)^2

√1.1025 = √

1.05 = 1 + r/2

0.05 = r/2

r = 0.10 = 10%

Alternate solution:

We see that the total interest earned for the year is 220,500 - 200,000 = $20,500. Since the interest is compounded semi-annually, we can make an educated guess that the interest earned for the first half of the year is $10,000 and that for the second half of the year is $10,500 (because of the effect of compounding interest).

Since 10,000/200,000 = 0.05 = 5%, we see that the interest rate for half the year is 5%; thus,the annual interest rate is doubled to 10%.

Answer: C

Fdambro294 · Answer

(1st) we know that the interest taken in 1 year at r% compound interest is going to be > the interest taken in 1 year at the same r% but at SIMPLE Interest

We can find the simple interest earned in 1 year at this r% easily by determining the Interest earned and dividing by the initial principal

(20,500) / (200,000) = (205) / (2,000) = (41) / (400) = (10.25) / (100)

Thus, if the interest were taken at simple interest over 1 year, the interest rate would have been 10.25%

To achieve the same amount, we do not need as high of an interest rate if taken semi-annually at Compound Interest.

At this point, the only answer that makes sense is (C) 10%, but we can check rather quickly to see if this is the correct answer

End first 6 months: (5%) of ($200,000) ——-> would be HALF of $20,000 ——-> $10,000

: new principal is $210, 000

End of year: 5% of ($210,000) is ——-> HALF of $21,000 ——> $10,500

Final balance: $200,000 + $10,000 + $10,500 = $22,500

(C) 10% is the correct answer

Posted from my mobile device

GMATGuruNY · Answer

On the GMAT, compounded interest is generally just a little more than simple interest.
If 20% simple interest yields X dollars, then 20% compounded interest will generally yield just a little more than X dollars.

Given an investment of $200,000, the interest earned here (20,500) is just a little more 10% simple interest (20,000).
Implication:
The value of r must be around 10%, implying that only answer choices C and D are viable.
Eliminate A, B, and E.

C: r=10
10% annual interest compounded semi-annually means that 5% interest is yielded every 6 months, as follows:
1st 6 months --> 200,000 + 5% of 200,000 = 200,000 + 10,000 = 210,000
2nd 6 months --> 210,000 + 5% of 210,000 = 210,000 + 10,500 = 220,500
Success!

C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

An investment of $200,000 in an instrument that returns an annual rate

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

An investment of $200,000 in an instrument that returns an annual rate

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards