Question

Elisha invests $7,100 at 5.8%. How much more can Elisha expect her investment to be worth after 3 years than at the beginning? Round to the nearest ten.(1 point)
earnings = $

Answer 1

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.