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Jamie deposits $627 into a savings account. The account has an interest rate of 3.5%, compounded quarterly. Write the function that gives the amount of money in dollars, J(t), in Jamie's account t years after the initial deposit.

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The function that gives the amount of money in dollars, J(t), in Jamie's account t years after the initial deposit is A = 627(1.00875)^{4t} (in dollars)

How to calculate compound interest's amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

For this case, we're given that:

  • Initial amount Jamie deposits = P = $627
  • Rate of interest = 3.5% compounding quarterly
  • Time = t years

Rate of interest is compounding quarterly.

Each year has 4 quarters.

Rate of interest is usually annual rate of interest. Since compounding is done quarterly, let we express everything in quarter years.

Quarterly interest rate compounding quarterly = 3.5/4 = 0.875% = R%

t years has 4t quarters = T

Thus, we get the final amount in Jamie's account as

[tex]A = P\left(1 +\dfrac{R}{100}\right)^T\\\\A = 627 \left(1 +\dfrac{0.875}{100}\right)^{4t}\\\\A = 627(1.00875)^{4t} \: \rm \text{(in dollars)}[/tex]

Thus, the function that gives the amount of money in dollars, J(t), in Jamie's account t years after the initial deposit is [tex]A = 627(1.00875)^{4t}[/tex] (in dollars)

Learn more about compound interest here:

https://brainly.com/question/11897800

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