Question

1. Suppose you invest $500 at 10% interest, compounded annually. After 5 years, how much money would you have in your account? Remember, the formula is A = P(1 + r)t.
2. If you invest $100 at 2% interest, compounded every 2 years, what would your balance be after 6 years?


4. Two friends are going on a road trip and are downloading podcasts to listen to on the drive. They choose two podcasts. They download A episodes of Podcast A, and B episodes of Podcast B. Each episode of Podcast A is x minutes long, and each episode of Podcast B is y minutes long. Tell what the following expressions represent in the situation.
a. Ax + By
b. A + B

Answer 1

Solution 1:

The compound interest formula to be used here is given by:

$A=P(1+r)^{t}$

Now we are given:

P=$500

r=10% or 0.1

t=5 years

Plugging them in the formula ,

$A=500(1+0.1)^{5}$

A=$802.255

Answer : After 5 years I will have $802.255 in my account.

Solution 2:

The formula for compound interest here is given by:

$A=P(1+\frac{r}{n})^{nt}$

Here interest is compounded after every two years, so n=2

r=2% or 0.02

t=6 years

P= $100

Plugging these into the formula:

$A=100(1+\frac{0.02}{2})^{2*6}$

$A=100(1+0.01)^{12}$

$A=100(1.01)^{12}$

A=$112.683

Answer: The balance after 6 years would be $112.683.

Solution 4:

In this situation:

a. Ax+By

Ax represents duration of Podcast A episodes

By represents duration of Podcast B episodes

Ax+By represents total duration of Podcast A and Podcast B songs.

b. A+B

A+B represents total number of episodes of Podcast A and Podcast B.