Question

(score for question 1: ___ of 4 points)

1. the graph shows two accounts with the same principal and annual interest rate. use the graph to estimate the answer to each question. show your work.

(a) about how much more compound interest than simple interest is earned after 35 years? remember to show your work.
(b) about how much more compound interest than simple interest is earned after 45 years? remember to show your work.
answer:

Explanation:

Part (a)

Step1: Find compound interest at 35 years

From the graph, the compound interest (dashed line) at \( x = 35 \) years has a \( y \)-value (total amount) of approximately \( \$900 \).

Step2: Find simple interest at 35 years

From the graph, the simple interest (solid line) at \( x = 35 \) years has a \( y \)-value (total amount) of approximately \( \$600 \).

Step3: Calculate the difference

Subtract the simple interest total from the compound interest total: \( 900 - 600 = 300 \).

Step1: Find compound interest at 45 years

From the graph, the compound interest (dashed line) at \( x = 45 \) years has a \( y \)-value (total amount) of approximately \( \$1200 \).

Step2: Find simple interest at 45 years

From the graph, the simple interest (solid line) at \( x = 45 \) years has a \( y \)-value (total amount) of approximately \( \$700 \).

Step3: Calculate the difference

Subtract the simple interest total from the compound interest total: \( 1200 - 700 = 500 \).

Answer:

About \(\$300\) more compound interest is earned after 35 years.

Part (b)