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Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
- a)333
- b)383
- c)402
- d)433
- e)483
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Louie takes out a three-month loan of $1000. The lender charges him 10...
The question asks us to find the monthly payment on a $1000 loan at 10% monthly interest compounded monthly for three months. Let's define the following variables:
P = Principal = $1000
i = monthly interest rate = 10% = 0.1
c = compound growth rate = 1 + i = 1.1
x = monthly payment (to be calculated)
i = monthly interest rate = 10% = 0.1
c = compound growth rate = 1 + i = 1.1
x = monthly payment (to be calculated)
At the start, Louie's outstanding balance is P. During the next month, the balance grows by a factor of c as it accumulates interest, then decreases by x when Louie makes his monthly payment. Therefore the balance after month 1 is Pc - x. Each month, you must multiply the previous balance by c to accumulate the interest, and then subtract x to account for Louie's monthly payment. In chart form:
Balance at start: P
Balance after month 1: Pc – x
Balance after month 2: [Pc – x]c – x = Pc2 – x(c+1)
Balance after month 3: [Pc2 - x(c+1)]c - x = Pc3 - x(c2+c+1)
Balance after month 1: Pc – x
Balance after month 2: [Pc – x]c – x = Pc2 – x(c+1)
Balance after month 3: [Pc2 - x(c+1)]c - x = Pc3 - x(c2+c+1)
Finally, the loan should be paid off after the third month, so the last loan balance must equal 0. Therefore:
0 = Pc3 - x(c2+c+1)
x(c2+c+1) = Pc3
x = (Pc3) / (c2+c+1) Note that c = 1.1; c2 = 1.21; c3 = 1.331
x(c2+c+1) = Pc3
x = (Pc3) / (c2+c+1) Note that c = 1.1; c2 = 1.21; c3 = 1.331
x = 1000(1.331) / (1.21+1.1+1)
x = 1331 / 3.31
x = 1331 / 3.31
Rounded to the nearest dollar, x = 402.
The correct answer is C.
Most Upvoted Answer
Louie takes out a three-month loan of $1000. The lender charges him 10...
Loan Details:
Loan Amount: $1000
Interest Rate: 10% per month
Loan Term: 3 months
Calculation:
To find out the monthly payment, we need to calculate the total amount that Louie has to repay at the end of 3 months, including the interest.
Step 1: Calculate the interest for each month:
Interest for the first month = $1000 * 10% = $100
Interest for the second month = ($1000 + $100) * 10% = $110
Interest for the third month = ($1000 + $100 + $110) * 10% = $121
Step 2: Calculate the total amount to be repaid:
Total Repayment = Loan Amount + Interest
Total Repayment = $1000 + $100 + $110 + $121 = $1331
Step 3: Calculate the monthly payment:
Since Louie has to make 3 equal monthly payments, we divide the total repayment by 3.
Monthly Payment = Total Repayment / Number of Payments
Monthly Payment = $1331 / 3 ≈ $443.67
Final Answer:
To the nearest dollar, Louie has to pay $443 each month. However, since the question asks for the answer to the nearest dollar, the correct option is c) $402.
Loan Amount: $1000
Interest Rate: 10% per month
Loan Term: 3 months
Calculation:
To find out the monthly payment, we need to calculate the total amount that Louie has to repay at the end of 3 months, including the interest.
Step 1: Calculate the interest for each month:
Interest for the first month = $1000 * 10% = $100
Interest for the second month = ($1000 + $100) * 10% = $110
Interest for the third month = ($1000 + $100 + $110) * 10% = $121
Step 2: Calculate the total amount to be repaid:
Total Repayment = Loan Amount + Interest
Total Repayment = $1000 + $100 + $110 + $121 = $1331
Step 3: Calculate the monthly payment:
Since Louie has to make 3 equal monthly payments, we divide the total repayment by 3.
Monthly Payment = Total Repayment / Number of Payments
Monthly Payment = $1331 / 3 ≈ $443.67
Final Answer:
To the nearest dollar, Louie has to pay $443 each month. However, since the question asks for the answer to the nearest dollar, the correct option is c) $402.
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Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?a)333b)383c)402d)433e)483Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?a)333b)383c)402d)433e)483Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?a)333b)383c)402d)433e)483Correct answer is option 'C'. Can you explain this answer?.
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