Question

Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent from her parents. She does not pay interest on the money she borrows from her parents.

a. Let f(t) represent the amount of money Tara owes in credit card debt, where t is the number of years after interest begins to accrue. Let g(t) represent the amount of money Tara owes to her parents, where t represents the number of years passed. Write a function (f + g)(t) to represent the total money that Tara owes.

b. How much will Tara have to repay if she continues this way without any repayment for 2 years? (SHOW WORK)

Answer 1

`(f + g)(t) = f(t) + g(t) = 14375 (1 + (5.3)/(100))^(t) + 6840t`

$29619.13

Explanation:

a. Tara has $14375 in credit card debt and the interest rate is 5.3%.

Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then

`f(t) = 14375 (1 + (5.3)/(100))^(t)` ......... (1)

Again Tara borrows $570 each month for rent from her parents without any interest.

If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write

g(t) = 570 × 12t = 6840t ........ (2)

Therefore,
`(f + g)(t) = f(t) + g(t) = 14375 (1 + (5.3)/(100))^(t) + 6840t`

b. So, for t = 2 years,

`(f + g)(t) = 14375 (1 + (5.3)/(100))^(2) + 6840 * 2` = $29619.13

So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)