To calculate the total amount of money you will pay back when you borrow $1,600 for 6 years at an annual interest rate of 10%, we can use the formula for simple interest, which is:
\[ \text{Total Amount} = P + I \]
where:
- \( P \) is the principal amount (the initial amount borrowed),
- \( I \) is the interest.
The interest can be calculated using the formula:
\[ I = P \times r \times t \]
where:
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time in years.
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Convert the interest rate into decimal form: \[ r = 10% = 0.10 \]
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Determine the principal amount and time: \[ P = 1600, \quad t = 6 \]
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Calculate the interest: \[ I = 1600 \times 0.10 \times 6 = 1600 \times 0.6 = 960 \]
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Calculate the total amount to be paid back: \[ \text{Total Amount} = P + I = 1600 + 960 = 2560 \]
Thus, the total amount of money you will pay back after 6 years is $2,560.