# A student borrows $800 at 5.3% annual interest compounded semiannually. How much does he owe after 4 years?

##### 2 Answers

#### Explanation:

For this type of question, we would use Compound Interest which is gaining interest continuously over a certain amount of years, instead of working them all out separately. The formula for Compound Interest is:

Where

Plugging in values:

We change this to

Plugging into calculator:

Rounding to 2 d.p:

Minusing the before value from the after value:

Rounding to 2 decimal places gives

#### Explanation:

Note that 'semiannually' means twice per year. So each year has 2 calculation cycles

You have to 'split up' the annual percentage into a proportion that reflects the calculation cycle.

So the annual interest of

The general form for this context is

where

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The amount owed is

Rounding to 2 decimal places gives