Question

There is $10 in an account that pays 5% interest per year. The interest is added to the total in the account at the end of each year. How much money will be in the account at the end of each year?

Total at the end of year 1:
Total at the end of year 2:
Total at the end of year 3:

Answer 1

Below in bold.

Explanation:

5% = 0.05.

At the end of year 1 , Total = 10 + 0.05*10 = $10.50.

At the end of year 2, Total = 10.50 + 0.05 * 10.5 = $11.03.

At the end of year 2, Total = 11.03 + 0.05 * 11.03 = $11.58.

Answer 2

• Total at the end of year 1 = $10.05

• Total at the end of year 2 = $11.03
• Total at the end of year 3 = $11.58

Explanation:

`Total\ after\ n\ year=capital*(100\%+interest\ per\ year)^n`

a. Total at the end of year 1

= $10 × (100% + 5%)

= $10.50

b. Total at the end of year 2

= $10 × (100% + 5%)²

= $10 × 1.1025

≈ $11.03

c. Total at the end of year 3

= $10 × (100% + 5%)³

= $10 × 1.157625

≈ $11.58