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Lewis and maria each take out a loan of £2000 at the same time. the loans have a compound interest rate of 3.5% per year. 2 years after taking out the loan, lewis pays back £1000 3 years after taking out the loan, maria pays back £1000 10 years after taking out the loan, how much more money does maria owe than lewis ?

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Final answer:

To determine how much more Maria owes than Lewis after 10 years with a compound interest rate of 3.5%, we must calculate the compounded amount for each, minus their respective repayments, and compare the totals. Maria's balance accrues one more year of interest on her repayment than Lewis due to their differing repayment schedules.

Step-by-step explanation:

The question involves calculating the amount owed by two individuals, Lewis and Maria, who have taken out the same loan amount with compound interest and make payments at different times. To determine how much more money Maria owes than Lewis 10 years after taking out a loan with a compound interest rate of 3.5%, we need to use the compound interest formula which is A = P(1 + r/n)^(nt), where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time in years.

First, we calculate the amount both parties owe after 10 years without considering their repayments. Then we subtract the repayments made by each at the specified times, taking into account that these repayments also stop interest from accumulating on the repaid amount. Be sure to adjust the principal accordingly after each repayment when recalculating the compound interest. Since the rates and timing of repayments differ, Maria's remaining balance would have accrued interest for one additional year compared to Lewis, resulting in her owing more.

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