Answer:
approximately $97.20.
Explanation:
To calculate the interest earned on a principal amount of $700 placed in a savings account with an annual interest rate of 1.3% compounded continuously after 10 years, you can use the formula for continuous compounding:
A = P * e^(rt)
Where:
A = the amount of money accumulated after a certain time, including the principal.
P = the principal amount ($700).
r = annual interest rate (1.3% or 0.013 as a decimal).
t = time in years (10 years).
e = the base of the natural logarithm (approximately 2.71828).
Let's plug in the values and calculate:
A = 700 * e^(0.013 * 10)
A = 700 * e^(0.13)
A ≈ 700 * 1.1388503
A ≈ $797.19521
Now, to find the interest earned, you can subtract the principal amount from the final amount:
Interest = A - P
Interest ≈ $797.19521 - $700
Interest ≈ $97.19521
So, the interest earned after 10 years in a savings account with an annual interest rate of 1.3% compounded continuously is approximately $97.20.