Determine the compound amount of a debt of $1,600,000 agreed at a rate of 6.5% compounded monthly for 4 years and 6 months.

1. Identify the principal, interest rate, compounding frequency, and time.

P = 1,600,000

r = \frac{6.5}{100} = 0.065

n = 12

t = 4.5 \text{ years}

2. Use the compound interest formula:

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

3. Calculate individual components:

\frac{r}{n} = \frac{0.065}{12} = 0.0054167

nt = 12 \times 4.5 = 54

4. Substitute into the formula:

A = 1,600,000 \left(1 + 0.0054167 \right)^{54}

5. Calculate the exponent:

6. Final calculation:

\boxed{A=2141944.99}