Question

The function 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

$3,689.40
$3,689.40

$414.16
$414.16

$401.31
$401.31

$10,157.66

Answer 1

[AI-generated answer — Bot GPT 3.5]

The balance of the account after 13 years can be found by plugging in n=13 into the function g(n):

g(13) = 275 * (1.032)^13
g(13) = 275 * 1.483774
g(13) = $407.793

Therefore, the balance of the account after 13 years is $407.79.

None of the given options are correct.

Answer 2

correct logic, but wrong final results

275 * (1.032)^13 = 275 * 1.506 = 414.16

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake in the calculation. You are correct!

The balance of the account after 13 years is:

275 * (1.032)^13 = 275 * 1.506 = $414.16

Therefore, the correct answer is $414.16. Thank you for catching that error.