5. Find the value of 25,000 invested at 7.5% for 11 years if it is compounded monthly Eqn __ Ans __

To find the future value of an investment compounded monthly, we use the compound interest formula:<br /><br />\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]<br /><br />where:<br />- \( A \) is the amount of money accumulated after n years, including interest.<br />- \( P \) is the principal amount (initial investment), which is \$25,000.<br />- \( r \) is the annual interest rate (decimal), so 7.5% becomes 0.075.<br />- \( n \) is the number of times that interest is compounded per year, which is 12 for monthly compounding.<br />- \( t \) is the time in years, which is 11.<br /><br />Plugging in the values:<br /><br />\[ A = 25000 \left(1 + \frac{0.075}{12}\right)^{12 \times 11} \]<br /><br />\[ A = 25000 \left(1 + 0.00625\right)^{132} \]<br /><br />\[ A = 25000 \left(1.00625\right)^{132} \]<br /><br />Now calculate:<br /><br />\[ A \approx 25000 \times 2.3196 \]<br /><br />\[ A \approx 57,990 \]<br /><br />So, the value of the investment after 11 years is approximately \$57,990.