Question

The amount of money, £P, in a savings account t years after 1st January 2011 is given by the formula `P = 6000 xx 1.05^t`. Does the account pay simple or compound interest. Explain how you know?

Answer 1

The account pays compound interest.

The whole of the previous amount is increased by `5%`

Explanation:

The account pays compound interest.

The clue is in the power of `t`

This would mean `6000 xx1.05xx1.05xx1.05xx....... t` times

`1.05 = 105/100 = 100% +5%`

So each time you multiply by `1.05` you are increasing the whole of the previous amount by `5%`

For example, if `t =5,` then `6000xx1.05^5` means

`color(blue)(6000 xx1.05)xx1.05xx1.05xx1.05xx1.05`

`=color(blue)(6300)xx1.05xx1.05xx1.05xx1.05`

`=6615xx1.05xx1.05xx1.05`

`=6945.75xx1.05xx1.05`

`=7293.0375 xx1.05`

`=7657.69`

Each line represents another increase by `5%`