Question

Jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit.

f(t)=2430(1.04)^28

a. rewrite the equation in the form f(t)=A(1+r/n)^nt

b. what is the annual interest rate?​

Answer 1

`f(t) = 2430(1 + (0.16)/(4) )^(7 * 4)`

The APR is 16%.

Explanation:

Jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit as

`f(t) = 2430(1.04)^(28)` ......... (1)

a. If we want to rewrite the equation in the form

`f(t) = A(1 + (r)/(n) )^(nt)` .......... (2)

Then comparing equation (1) and (2) we get, A = 2430 and t = 7

Hence, 7n = 28

⇒ n = 4

Now,
`1 + (r)/(4) = 1.04`

⇒ r = 0.16 i.e. 16%

Therefore, the expression is

`f(t) = 2430(1 + (0.16)/(4) )^(7 * 4)` (Answer)

b. The APR is 16%. (Answer)