A business needs a $240,000 loan for one year and has two options to

Question

A business needs a $240,000 loan for one year and has two options to decide between. Option 1 is a fixed rate loan for the entire amount, with a simple annual interest rate of 5%. Option 2 involves two loans: a fixed rate loan for $190,000, with a simple annual interest rate of 4%, and a second fixed rate loan for $50,000, with a simple annual interest rate of r%. Both options have otherwise identical terms and require payment in full of interest and principal at the end of the year.

In the first column, identify the interest rate r% at which the two options require the same total interest payment. In the second column, identify the interest rate r% at which the annual interest on the $190,000 loan in Option 2 would be exactly twice the annual interest on the $50,000 loan. Make only two selections, one in each column.

OprBarbosa2017 · Answer

i want to know the answer for this question
i got  8.8%  for first column and  7.6%  for second column

Apt0810 · Answer

1)8.8%, since both the options have equal interest so:
240000*5= 190000*4 + 50000*r
r=8.8%
2)190000*4 =2*50000*r, so r=7.6%

Posted from my mobile device

Sajjad1994 · Answer

Official Explanation

First, find the interest rate at which the two options have equal total interest payments.

Interest on Loan 1:

5% of $240,000 = 0.05 × $240,000 = $12,000

Alternatively, find 10% and divide by 2 to get 5%: 10% of 240,000 = 24,000. Half of that is 12,000.
 
 Interest on Loan 2:

4% of $190,000 = 0.04 × $190,000 = $7,600

r% of  $50,000=\frac{r}{100}×$50,000=$500r

For the total interest payment on Option 1 to be equal to the total interest payment on Option 2, the sum of the interest on the $50,000 loan and the interest on the $190,000 loan must be equal to the interest payment on the $240,000 loan. Set up that equation and solve.

500r + 7,600 = 12,000

500r = 12,000 – 7,600

500r = 4,400

r = 8.8
 
Next, calculate the interest rate at which the interest payment on the $190,000 loan (at 4%) would be equal to twice the interest payment on the $50,000 loan (at r%). Reuse the numbers already calculated during the first half of this problem.

interest on 190k loan = 2(interest on 50k loan)

7,600 = 2(500r)

7,600 = 1,000r

r = 7.6
 
  Column 1: The correct answer is (E).
Column 2: The correct answer is (D).

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.

Same total interest payments	$190,000 loan requires twice the interest	Interest rate r%
		4.4%
		5.2%
		6.1%
		7.6%
		8.8%
		9.5%

A business needs a $240,000 loan for one year and has two options to

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 Two-part Analysis (TPA) Questions

A business needs a $240,000 loan for one year and has two options to

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