The function g(n)=275(1.032)n

Question

𝑔
(
𝑛
)
=
275
(
1.032
)
𝑛
models the sequence of the end-of-year balance of an investment account with a principal of $275 and a 3.2 percent compound annual interest rate, in which n is the length of the investment in years. Find the balance of the account after 13 years.(1 point)
Responses

$414.16
$414.16

$401.31
$401.31

$10,157.66
$10,157.66

$3,689.40

Answer 1

To find the balance of the investment account after 13 years using the function \( g(n) = 275(1.032)^n \), we need to substitute \( n = 13 \) into the equation.

\[ g(13) = 275(1.032)^{13} \]

Calculating \( (1.032)^{13} \):

\[ (1.032)^{13} \approx 1.4575 \quad \text{(using a calculator)} \]

Now, we can calculate \( g(13) \):

\[ g(13) = 275 \times 1.4575 \approx 401.31 \]

Thus, the balance of the account after 13 years is approximately $401.31.