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MMLU / Alex needs to borrow 10, 000 from the bank. The bank gives him two options.…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Alex needs to borrow $10,000\$10,\!000 from the bank. The bank gives him two options. 1. A ten-year loan with an annual interest rate of 10%10\% compounded quarterly, with the condition that at the end of 5 years, Alex must make a payment equal to half of what he owes. The other half continues to accrue interest, and at the end of the ten years, Alex will pay off the remaining balance. 2. A ten-year loan with a simple annual interest rate of 12%12\%, with just one lump-sum payment at the end of the ten years. Find the positive difference between the total amounts Alex has to pay back under the two schemes. Round your answer to the nearest dollar.
Plain-text mathematical notation (without MathML)
Alex needs to borrow $10, 000 from the bank. The bank gives him two options. 1. A ten-year loan with an annual interest rate of 10% compounded quarterly, with the condition that at the end of 5 years, Alex must make a payment equal to half of what he owes. The other half continues to accrue interest, and at the end of the ten years, Alex will pay off the remaining balance. 2. A ten-year loan with a simple annual interest rate of 12%, with just one lump-sum payment at the end of the ten years. Find the positive difference between the total amounts Alex has to pay back under the two schemes. Round your answer to the nearest dollar.
Original LaTeX notation
Alex needs to borrow $\$10,\!000$ from the bank. The bank gives him two options. 1. A ten-year loan with an annual interest rate of $10\%$ compounded quarterly, with the condition that at the end of 5 years, Alex must make a payment equal to half of what he owes. The other half continues to accrue interest, and at the end of the ten years, Alex will pay off the remaining balance. 2. A ten-year loan with a simple annual interest rate of $12\%$, with just one lump-sum payment at the end of the ten years. Find the positive difference between the total amounts Alex has to pay back under the two schemes. Round your answer to the nearest dollar.

choices

  1. 16401
  2. 16400
  3. 382
  4. 383

subject

high_school_mathematics

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Source and history

task_id
6a635629-c2f2-5799-93de-9c71021bb41a
task_key
all--test--6a635629-c2f2-5799-93de-9c71021bb41a
task_revision_id
1
config / split
all / test

Official source

initial import