To calculate how much more Elisha's investment will be worth after 3 years, we can use the formula for compound interest:
\[ A = P(1 + r)^t \]
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).
- \( t \) is the time the money is invested for in years.
Given:
- \( P = 7,100 \)
- \( r = 5.8% = 0.058 \)
- \( t = 3 \)
Plugging the values into the formula:
\[ A = 7100(1 + 0.058)^3 \]
First, calculate \( (1 + 0.058)^3 \):
\[ 1.058^3 \approx 1.185 \]
Now calculate \( A \):
\[ A \approx 7100 \times 1.185 \approx 8,413.5 \]
To find out how much more Elisha can expect her investment to be worth after 3 years than at the beginning, we subtract the initial investment from the final amount:
\[ Earnings = A - P = 8,413.5 - 7,100 \approx 1,313.5 \]
Rounding to the nearest ten:
\[ Earnings \approx 1,310 \]
So, Elisha can expect her investment to be worth approximately $1,310 more after 3 years.
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