To estimate the total amount of the investment account after 32 years, we can analyze how much the principal of $1,500 increases every 10 years. Given that the investment increases 1.5 times every 10 years, we can calculate the investment amount at different intervals.
After 10 years: \[ 1,500 \times 1.5 = 2,250 \]
After 20 years: \[ 2,250 \times 1.5 = 3,375 \]
After 30 years: \[ 3,375 \times 1.5 = 5,062.50 \]
Since we need the estimation for 32 years, we can consider that 32 years is 2 years past 30. Assuming the growth continues at a similar rate, we estimate the amount for those additional 2 years (noting that it would still be a rough estimate).
The growth in the first 10-year period is about 50% of the 10-year cycle increase. To simplify, if we take a percentage of the last value:
Let's estimate that the growth during those 2 years would be roughly between the two 10-year increments. If it increases around 5% each year (a rough approximation derived from the 1.5x increase), for 2 years that would be: \[ 5,062.50 \times 0.05 \times 2 = 506.25 \]
Adding this small increase to the amount after 30 years: \[ 5,062.50 + 506.25 \approx 5,568.75 \]
Since we are estimating based on the provided options, it would be fair to round to the nearest option available. Among the given choices, $5,500 is the closest estimate.
Therefore, the estimated total amount of the account if $1,500 is invested for 32 years is:
$5,500