Find the compound amount and the amount of interest earned by the following deposit.
$9,000 at 7.57% compounded continuously for 5 years.
Using the formula for continuous compounding:
A = Pe^(rt)
where A is the final amount, P is the principal (starting amount), e is the natural logarithmic constant (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.
Plugging in the values given:
A = 9000e^(0.0757*5)
A = 12,742.51
So the compound amount is $12,742.51 after 5 years of continuous compounding.
To find the amount of interest earned, we subtract the initial amount from the final amount:
Interest = 12,742.51 - 9,000
Interest = $3,742.51
Therefore, the amount of interest earned on the $9,000 deposit at 7.57% compounded continuously for 5 years is $3,742.51.