To find out how much money Bert should deposit in order to earn exactly $144 in interest after 3 years with a simple interest rate of 1.6%, we can use the formula for simple interest:
\[ I = P \times r \times t \]
where:
- \( I \) is the interest earned,
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the yearly interest rate (in decimal form),
- \( t \) is the time in years.
Given:
- \( I = 144 \) dollars,
- \( r = 1.6% = 0.016 \),
- \( t = 3 \) years,
we need to solve for \( P \).
Substituting the values into the formula:
\[ 144 = P \times 0.016 \times 3 \]
Calculating \( 0.016 \times 3 \):
\[ 0.016 \times 3 = 0.048 \]
Now the equation becomes:
\[ 144 = P \times 0.048 \]
To find \( P \), divide both sides by \( 0.048 \):
\[ P = \frac{144}{0.048} \]
Now performing the division:
\[ P = 3000 \]
Therefore, Bert should deposit $3,000 to earn exactly $144 in interest after 3 years at a rate of 1.6%.
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