Question
You open a savings account that will yield 4.5% yearly compound interest. your first deposit is $550 and you don't deposit or withdraw anything for 3 years. What would be the function equation?
Answers
GPT 3.5
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case, the principal investment amount (P) is $550, the annual interest rate (r) is 4.5% or 0.045, the interest is compounded yearly (n = 1), and the time the money is invested for (t) is 3 years.
Putting these values into the formula, we get:
A = 550(1 + 0.045/1)^(1*3)
A = 550(1.045)^3
A = 550(1.142245)
A = $627.74
Therefore, the future value of the savings account after 3 years would be $627.74. The function equation for this scenario is:
A = 550(1.045)^t
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case, the principal investment amount (P) is $550, the annual interest rate (r) is 4.5% or 0.045, the interest is compounded yearly (n = 1), and the time the money is invested for (t) is 3 years.
Putting these values into the formula, we get:
A = 550(1 + 0.045/1)^(1*3)
A = 550(1.045)^3
A = 550(1.142245)
A = $627.74
Therefore, the future value of the savings account after 3 years would be $627.74. The function equation for this scenario is:
A = 550(1.045)^t