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ravis invested $9,250 in an account that pays 6 percent simple interest. How much morecould he have earned over 7 years if the interest had compounded weekly?

Question

ravis invested $9,250 in an account that pays 6 percent simple interest. How much morecould he have earned over 7 years if the interest had compounded weekly?

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Solution

To answer this question, we first need to calculate the amount of money Ravis would have earned with simple interest, and then compare it to the amount he would have earned with weekly compounded interest.

  1. Calculate Simple Interest: The formula for simple interest is I = PRT, where P is the principal amount, R is the rate of interest, and T is the time in years.

    I = 9,2506/1007=9,250 * 6/100 * 7 = 3,885

  2. Calculate Compounded Interest: The formula for compounded interest 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, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

    Here, interest is compounded weekly, so n = 52 weeks in a year.

    A = 9,250(1+0.06/52)(527)=9,250 * (1 + 0.06/52)^(52*7) = 13,789.49

  3. Subtract the simple interest from the compounded interest to find out how much more he could have earned.

    13,789.4913,789.49 - 9,250 - 3,885=3,885 = 654.49

So, Ravis could have earned $654.49 more over 7 years if the interest had compounded weekly.

This problem has been solved

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