Question

Louie Foster invested $4,500 at 3% interest compounded semiannually for 2 years

Answer 1

`\huge\boxed{5064.79 (2d.p)}`

Useful Information:

The formula for compound interest is:
`\sf{amount*decimal^{{No. calculations}}`

Explanation:

This is an example of compound percentage increase.

To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 3% by 100, this gives you 0.03. This is because percentages are out of 100 and so dividing the value by 100 gives you the percentage as a part of 1.

The next step is to add 1 to 0.03, this gives you 1.03. This is because you are working out the percentage increase.

The penultimate step is to work out the number of times that the new amount would need to be calculated. This can be done by multiplying 2 by 2, which gives you 4. This is because it will be compounded semiannually, which is twice a year.

The fnal step is to work out the total amount you would need to multiply the amount of 4,500 by 1.03 to the power of 4, this gives you 5064.79 (2 D.P). This is because you are working out 3% of the amount, and then adding it to the new amount and then finding 3% of that amount, and so on.

1) Divide 3% by 100.

`(3)/(100)=0.03`

2) Add 1 to 0.03.

`1+0.03=1.03`

3) Multiply 2 by 2.

`2*2=4`

4) Multiplly 4500 by 1.03 to the power of 4.

`4500*1.03^(4)=5064.79 (2 d.p)`