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

Answer:

$f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}$

The APR is 16%.

Step-by-step 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  

$f(t) = A(1 + \frac{r}{n} )^{nt}$ .......... (2)

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

Hence, 7n = 28

⇒ n = 4

Now, $1 + \frac{r}{4} = 1.04$

⇒ r = 0.16 i.e. 16%  

Therefore, the expression is  

$f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}$ (Answer)

b. The APR is 16%. (Answer)