question 14 of 18 (1 point) | question attempt 1 of 1\nalicia invested $35,000. each year, 6% of the current…

question 14 of 18 (1 point) | question attempt 1 of 1\nalicia invested $35,000. each year, 6% of the current year’s account value is earned in interest (compound interest).\npart 1 of 2\n(a) what growth factor will be used to calculate the amount of interest each year?\nthe growth factor is 1.06.\npart: 1 / 2\npart 2 of 2\n(b) what will be the total value of the account after eight years? round to the nearest cent.\nthe total value of the account after eight years will be $

question 14 of 18 (1 point) | question attempt 1 of 1\nalicia invested $35,000. each year, 6% of the current year’s account value is earned in interest (compound interest).\npart 1 of 2\n(a) what growth factor will be used to calculate the amount of interest each year?\nthe growth factor is 1.06.\npart: 1 / 2\npart 2 of 2\n(b) what will be the total value of the account after eight years? round to the nearest cent.\nthe total value of the account after eight years will be $

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate as a decimal, and $n$ is the number of years. Here, $P=$35000$, $r = 0.06$, and $n = 8$.

Step2: Substitute values into formula

$A=35000\times(1 + 0.06)^8$. First, calculate $(1 + 0.06)^8$. Using a calculator, $(1.06)^8=1.59384807453$. Then, multiply by the principal: $A = 35000\times1.59384807453$. $A=55784.68260855$.

Step3: Round to the nearest cent

Rounding $55784.68260855$ to the nearest cent gives $A=$55784.68$.

Answer:

$55784.68$