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? f(x) and how much would it be for the 4th, 5th, and 6th year?

Answer 1

The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of compounding periods per year
t = the number of years the money is invested for

Given:
P = $550
r = 4.5% or 0.045
n = 1 (compounded annually)
t = 3 years

Substitute these values into the formula:

A = 550(1 + 0.045/1)^(1*3)
A = 550(1.045)^3
A = 550(1.158515625)
A = $637.684375

So the function equation f(x) would be:

f(x) = 550(1.045)^x

To find the amount for the 4th, 5th, and 6th year, we can continue plugging in the respective values for x:

For the 4th year (x = 4):
f(4) = 550(1.045)^4
f(4) = 550(1.194003938)
f(4) = $656.2021659

For the 5th year (x = 5):
f(5) = 550(1.045)^5
f(5) = 550(1.248804781)
f(5) = $686.3426296

For the 6th year (x = 6):
f(6) = 550(1.045)^6
f(6) = 550(1.30418902)
f(6) = $717.3034628

Therefore, the amounts for the 4th, 5th, and 6th year would be $656.20, $686.34, and $717.30, respectively.