Question

You put $425 Into a savings account that earned 8% annual interest compounded quarterly a) Write a function that represents the balance of the account after t years. b) How much money will you have in the account after 6 years? (Be sure to round appropriately, this is money!) ​

Answer 1

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Answer:

  a)  f(t) = 425(1.02)^(4t)

  b)  $683.59

Step-by-step explanation:

a) The compound interest formula is ...

  A = P(1 +r/n)^(nt)

giving the balance A of an investment of principal P for t years at annual rate r compounded n times per year.

We have P = 425, r=0.08, and n=4, so we can write the function f(t) as ...

  f(t) = 425(1+0.08/4)^(4t)

  f(t) = 425(1.02)^(4t)

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b) The balance after 6 years is ...

  f(6) = 425(1.02^(4·6)) = 425(1.02^24) = 683.59

The account balance after 6 year will be $683.59.