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Perry borrowed $10,846 at 12% ordinary interest for 89 days. On day 33 of the loan, he made a partial payment of $3,531. What is the maturity value of the loan?  Do not round off values in intermediate calculations.Round off only the final answer to the nearest dollar.Do not include currency sign in the answer.Number format: [Ex. 2,540]- No space between numbers- Use comma as thousands separator

Question

Perry borrowed 10,846at1210,846 at 12% ordinary interest for 89 days. On day 33 of the loan, he made a partial payment of 3,531. What is the maturity value of the loan?  Do not round off values in intermediate calculations.Round off only the final answer to the nearest dollar.Do not include currency sign in the answer.Number format: [Ex. 2,540]- No space between numbers- Use comma as thousands separator

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Solution

To calculate the maturity value of the loan, we first need to calculate the interest on the original loan and then subtract the interest saved by the partial payment. Here are the steps:

  1. Calculate the interest on the original loan: Interest = Principal * Rate * Time = 10,846∗12/100∗89/365=10,846 * 12/100 * 89/365 = 267.94

  2. Calculate the interest saved by the partial payment: Interest saved = Partial payment * Rate * Time remaining = 3,531∗12/100∗(89−33)/365=3,531 * 12/100 * (89-33)/365 = 48.36

  3. Subtract the interest saved from the original interest to get the total interest: Total interest = Original interest - Interest saved = 267.94−267.94 - 48.36 = $219.58

  4. Add the total interest to the original loan minus the partial payment to get the maturity value: Maturity value = (Original loan - Partial payment) + Total interest = (10,846−10,846 - 3,531) + 219.58=219.58 = 7,534.58

Rounding off to the nearest dollar, the maturity value of the loan is $7,535.

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