Can you provide a scenario question involving compound interest and explain how to solve it?

Scenario: Sarah deposits $5000 into a savings account that earns 5% interest compounded annually. How much money will she have in the account after 3 years?

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for

In this scenario:
P = $5000
r = 0.05 (5% interest rate)
n = 1 (compounded annually)
t = 3 years

Plugging these values into the formula:

A = $5000(1 + 0.05/1)^(1*3)
A = $5000(1 + 0.05)^3
A = $5000(1.05)^3
A = $5000(1.157625)
A = $5788.13

Therefore, Sarah will have $5788.13 in the savings account after 3 years.

Scenario:

You invest $1,000 at an annual interest rate of 5%, compounded annually.

Question:

How much will your investment be worth after 10 years?

Solution:

Use the formula for compound interest:

```
A = P(1 + r/n)^(nt)
```

where:

- A = future value of the investment
- P = principal (original investment)
- r = annual interest rate as a decimal
- n = number of times compounded per year
- t = number of years

In this case:

- P = $1,000
- r = 0.05
- n = 1 (compounded annually)
- t = 10

```
A = 1000(1 + 0.05/1)^(1-10)
A = 1000(1.05)^10
A = $1,628.89
```

Therefore, after 10 years, your investment will be worth $1,628.89.