Questions: Dominic invested 19,000 in an account paying an interest rate of 6.1% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 16 years?

Solution Steps

Let \( P = 19000 \) (the principal amount), \( r = 0.061 \) (the annual interest rate), \( n = 12 \) (the number of times interest is compounded per year), and \( t = 16 \) (the time in years).

Use the compound interest formula:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Substituting the identified variables into the formula gives:

\[ A = 19000 \left(1 + \frac{0.061}{12}\right)^{12 \times 16} \]

Calculate the value of \( A \) using the expression derived in Step 2:

\[ A = 19000 \left(1 + \frac{0.061}{12}\right)^{192} \]

After performing the calculations, round \( A \) to the nearest dollar to find the total amount in the account after 16 years.

\[ A \approx 50298 \]

Final Answer