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Over a period of 300 days, Shawna Johnson earned $450 interest in a retirement account paying interest at a rate of 5%. Find the amount in the account at the end of 300 days.

User AXO
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2 Answers

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Final answer:

To find the principal amount in Shawna Johnson's retirement account, we need to use the simple interest formula, convert the time from days to years, and then rearrange the formula to calculate the principal. After finding the principal, add the interest earned to determine the total amount in the account.

Step-by-step explanation:

Finding the Principal Amount from Simple Interest

In order to find the amount in Shawna Johnson's retirement account at the end of 300 days, given that she earned $450 in interest at a rate of 5%, we first need to use the formula for simple interest: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years. Since we know the interest I ($450), the annual interest rate r (5%), and the time t (300 days is roughly 300/365 years), we can rearrange the formula to solve for P (the principal amount). The steps are as follows:

  1. Convert the time period from days to years: t = 300/365.
  2. Rearrange the formula to solve for P: P = I / (r * t).
  3. Plug the values into the equation and solve for P.

Simplifying the equation during step 3, we can find the principal amount to which interest was applied. After calculating P, we add the interest earned to P to get the final amount in the account at the end of 300 days.

User Rajibdotnet
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24 votes
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She earned 300/365 *5% =4.1%
Beginning balance equals 450/.041=10,976
Ending balance = 10,976+450=11,425
User TWL
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