Question

Philip deposited $1,200 in a bank that is paying 9% interest rate once a year. Select a function for P representing the amount of money he’ll have after T years

P= 1.09t
P= 1,200(1.0075)t
P=1,200(1.09)t
P=1,200(0.09)t
P=1,200e^0.09t

Answer 1

Option C

The function for P representing the amount of money Philip will have after T years p = 1200(1.09)t

Solution:

Given, Philip deposited $1,200 in a bank that is paying 9% interest rate once a year.

We have to select a function for P representing the amount of money he’ll have after T years .

Now, let us calculate amount after 1 year, then t = 1, rate = 9% =
`(9)/(100)` =0.09, amount = $1200.

Amount in bank after 1 year = amount deposited + interest gained

⇒1200 + 1200 x 0.09 x 1 ⇒ 1200(1 + 0.09)

⇒Hence our answer is 1200(1.09)

Now, put t = 1 in given options.

P= 1.09t ⇒ p = 1.09 ⇒ doesn’t match with our answer.

P= 1,200(1.0075)t ⇒ p = 1200(1.0075) ⇒ doesn’t match with our answer.

P=1,200(1.09)t ⇒ p = 1200(1.09) ⇒ matches with our answer.

P=1,200(0.09)t ⇒ p = 1200(0.09) ⇒ doesn’t match with our answer.

P=1,200e^0.09t ⇒ p = 1200e^0.09 ⇒ doesn’t match with our answer.

Hence, the correct representation is p = 1200(1.09)t. Thus option C is correct