$11,700 is invested in a compound interest account paying 3.9% compounded quarterly. How much will be in the account after 18 years? Round your answer to the nearest cent.
evaluate
11700(1 + .039/4)^72
23527.940563
An isotope of protactinium undergoes radioactive changes at an exponential rate, having a half-life of 32,760 years. Determine the number of grams that will remain 2,000 years from a 120-gram sample using the function
To calculate the future value of an investment with compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal (P) is $11,700, the annual interest rate (r) is 3.9% or 0.039 as a decimal, the interest is compounded quarterly (n = 4), and the investment period (t) is 18 years.
Plugging the values into the formula, we get:
A = 11700(1 + 0.039/4)^(4*18)
Calculating this expression, we get:
A ≈ 11700(1 + 0.00975)^72
A ≈ 11700(1.00975)^72
Using a calculator, we find:
A ≈ 11700(1.744365793)
A ≈ 20401.28
Therefore, the amount in the account after 18 years will be approximately $20,401.28.