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%

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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).

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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

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