Write a compount interest function to model each situation. Then find the balance after the given number of years
$27,000 invested at a rate of 3.75% compounded quarterly; 3 years
i = .0375/4 = .009375
n = 3(4) = 12
amount = 27000(1.009375)^12 = ....
To write a compound interest function, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (balance)
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
For the given situation:
Principal amount (P): $27,000
Annual interest rate (r): 3.75% or 0.0375 (as a decimal)
Number of times interest is compounded per year (n): quarterly, which means 4 times
Number of years (t): 3
Now we can plug in these values into the compound interest formula:
A = 27000(1 + 0.0375/4)^(4*3)
Let's calculate it to find the balance after 3 years:
A = 27000(1 + 0.009375)^(12)
A = 27000(1.009375)^(12)
A ≈ 27000(1.115529168)
A ≈ 30126.70
Therefore, the balance after 3 years would be approximately $30,126.70.