The question is a little unclear. I'm not certain if they meant

A compound interest of 2.7%...
...every half-yearly

or

A compound interest of...
...(2.7% every half-yearly).

Going by the first case, the rate every half a year is 1.35% and then there are a total of 10 half-years, so the formula for the final sum is

A = 15000 (1 + 1.35/100)^10
Subtract 15000 from this value to find the interest earned (I have no calculator with me now)

Going by the second case, the rate every half a year is 2.7% and then there are a total of 10 half-years, so the formula for the final sum is

A = 15000 (1 + 2.7/100)^10
Subtract 15000 from this value to find the interest earned (I have no calculator with me now)

Sounds more like case 2.

'pays 2.7% interest every half-yearly' basically means '2.7%/½year'.

The first case would be phrased as 'interest of 2.7%/annum or 2.7%/per year, compounded every half-yearly'

Sorry I do get it.... and what's the difference between compound and simple interest?

https://www.investopedia.com/ask/answers/042315/what-difference-between-compounding-interest-and-simple-interest.


To quote,

Simple interest is based on the principal amount of a loan or deposit.

In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.

Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

Ohh I get now :)) thank uu

To give an example :

●Interest rate of 5%/year
●Principal sum $1000
●Deposit for 2 years

① If simple interest :

That 5% is always on the original amount only.

So total amount after 2 years
= $(1000 x 0.05) interest for year 1 + $(1000 x 0.05) interest for year 2 + original $1000
= $50 + $50 + $1000
= $50 × 2 + $1000
= $100 + $1000
= $1100


② If compound interest :

That 5% is on the latest accumulated total amount.

Total amount after 1 year
= $1000 x 1.05
= $1050

Total amount in the second year
= $1050 × 1.05
= $1102.50

This can be rewritten as :

$1102.50
= $(1000 × 1.05 x 1.05)
= $1000(1.05)²
= $1000(1 + 5/100)² → the formula for compound interest

Or you can use bacteria to think of the idea.

Suppose you start with 1000 bacteria at a certain time. Now, after 1 hour, the number of bacteria grows to 1050, an increase of 5%.

In the next hour, do you think the increase in bacteria is 50, or will it be more?

Bacteria growth is equal in all types of bacteria (including newly generated bacteria - they grow just like other bacteria) so the additional 50 bacteria formed in the first hour will also grow as well.

This is what it means by compounding - everything at the moment, including what has been formed, will be subject to another round of interest.

Not quite accurate.

Bacteria reproduce by binary fission, so if your 1000 bacteria only generates 50 more in 1 hour, then the growth rate is not equal across the entire 1000. (i.e some divided and some didn't)

So for the next hour, you won't be sure if more division will still be at 1.05 times.

In this 2nd hour, newly generated bacteria may or may not divide, previously divided parent bacteria may or may not divide, and those that didn't divide in the first hour may or may not divide as well.

Thank u for giving me e.gs. they are very elaborate and I rlly appreciate it :)

Just a heads up , bacteria growth models typically use e^t or 2^t as part of the equation