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Addison invested $950 in an account paying an interest rate of 1, one eigth1 81​ % compounded annually. Alexandra invested $950 in an account paying an interest rate of 0, one half0 21​ % compounded daily. After 5 years, how much more money would Addison have in her account than Alexandra, to the nearest dollar?

Question

Addison invested 950inanaccountpayinganinterestrateof1,oneeigth181950 in an account paying an interest rate of 1, one eigth1 81​ % compounded annually. Alexandra invested 950 in an account paying an interest rate of 0, one half0 21​ % compounded daily. After 5 years, how much more money would Addison have in her account than Alexandra, to the nearest dollar?

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Solution

The question seems to have some typographical errors in the interest rates. However, I'll assume that Addison's interest rate is 1.81% compounded annually and Alexandra's interest rate is 0.21% compounded daily.

Here's how you can calculate it:

Step 1: Convert the interest rates from percentages to decimals. So, 1.81% becomes 0.0181 and 0.21% becomes 0.0021.

Step 2: Calculate the amount in Addison's account after 5 years using the formula for compound interest: 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 (in decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested for, in years.

For Addison, since the interest is compounded annually, n = 1. So, her account balance would be A = 950(1 + 0.0181/1)^(1*5) = $1,089.47 (rounded to the nearest cent).

Step 3: Calculate the amount in Alexandra's account. Since her interest is compounded daily, n = 365. So, her account balance would be A = 950(1 + 0.0021/365)^(365*5) = $1,010.53 (rounded to the nearest cent).

Step 4: Subtract Alexandra's balance from Addison's to find out how much more money Addison would have. So, 1,089.471,089.47 - 1,010.53 = $78.94.

So, to the nearest dollar, Addison would have $79 more in her account than Alexandra after 5 years.

This problem has been solved

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