a business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. after 30 years, the…

a business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. after 30 years, the value of the bond will be $25,084.20. if the business owners investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?\n$345.31\n$318.22\n$286.74\n$228.59

a business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. after 30 years, the value of the bond will be $25,084.20. if the business owners investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?\n$345.31\n$318.22\n$286.74\n$228.59

Answer

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $t$ is the number of years, and $A$ is the amount of money in the account after $t$ years. Given $P=$7000$, $r = 0.043$, and $t = 30$.

Step2: Calculate the amount with continuous - compounding

Substitute the values into the formula: $A=7000\times e^{0.043\times30}$. First, calculate the exponent: $0.043\times30 = 1.29$. Then, find $e^{1.29}\approx3.6347$. So, $A = 7000\times3.6347=$25442.9$.

Step3: Calculate the difference

The value of the bond when compounded semiannually is $A_{semi}=$25084.20$. The difference $\Delta A=A - A_{semi}=25442.9 - 25084.20=$358.7$. There may be a small rounding - error difference in the provided options. The closest value to our calculated result is $$345.31$.

Answer:

$345.31$