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Sagot :
To find the account balance [tex]\( A \)[/tex] using the compound interest formula, we can use the following equation:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount, which is \[tex]$110,000. - \( r \) is the annual interest rate (in decimal form). Given as 1.5%, we convert this to a decimal by dividing by 100, so \( r = \frac{1.5}{100} = 0.015 \). - \( n \) is the number of times the interest is compounded per year. Since it is compounded annually, \( n = 1 \). - \( t \) is the time the money is invested for, in years. Given \( t = 10 \) years. Now, substituting the values into the compound interest formula: \[ A = 110000 \left(1 + \frac{0.015}{1}\right)^{1 \cdot 10} \] Simplify the inside of the parentheses first: \[ 1 + \frac{0.015}{1} = 1.015 \] Next, raise this number to the power of \((1 \cdot 10)\): \[ (1.015)^{10} \] Now, to get the final balance \( A \): \[ A = 110000 \times (1.015)^{10} \approx 110000 \times 1.160538 \approx 127659.49\] So, the account balance with the given conditions after 10 years is approximately: \[ A \approx \$[/tex]127,659.49 \]
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount, which is \[tex]$110,000. - \( r \) is the annual interest rate (in decimal form). Given as 1.5%, we convert this to a decimal by dividing by 100, so \( r = \frac{1.5}{100} = 0.015 \). - \( n \) is the number of times the interest is compounded per year. Since it is compounded annually, \( n = 1 \). - \( t \) is the time the money is invested for, in years. Given \( t = 10 \) years. Now, substituting the values into the compound interest formula: \[ A = 110000 \left(1 + \frac{0.015}{1}\right)^{1 \cdot 10} \] Simplify the inside of the parentheses first: \[ 1 + \frac{0.015}{1} = 1.015 \] Next, raise this number to the power of \((1 \cdot 10)\): \[ (1.015)^{10} \] Now, to get the final balance \( A \): \[ A = 110000 \times (1.015)^{10} \approx 110000 \times 1.160538 \approx 127659.49\] So, the account balance with the given conditions after 10 years is approximately: \[ A \approx \$[/tex]127,659.49 \]
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