Simple Interest and Compound Interest

With simple interest, the same interest is earned on the original £200 every year.

One year's interest: $200\times 0.04=\pounds 8$.

Over 5 years: $8\times 5=\pounds 40$.

The total interest is £40. Note that $4\%$ of £200 is £8 a year, not a flat £4, and that the question asks for the interest earned, not the final balance: the account would hold $200+40=\pounds 240$.

With simple interest, each year's interest is worked out on the original £300.

One year's interest: $300\times 0.04=\pounds 12$.

Over 3 years: $12\times 3=\pounds 36$.

The total interest is £36. Two things to watch: multiply by all 3 years, and give the interest, not the final balance of $300+36=\pounds 336$. (If the interest had been compound, the balance would be $300\times 1.04^3=\pounds 337.46$, so £37.46 of interest, slightly more.)

With compound interest the balance is multiplied by $1.05$ each year.

After year 1: $500\times 1.05=\pounds 525$.

After year 2: $525\times 1.05=\pounds 551.25$.

In one step: $500\times 1.05^2=\pounds 551.25$.

The total amount is £551.25, the whole balance, not the £51.25 of interest on its own. Compare this with simple interest, which would add £25 twice to give £550. Compounding earns an extra £1.25 because year 2's interest is worked out on £525, not £500.

With simple interest, each year's interest is worked out on the original £1000.

One year's interest: $1000\times 0.05=\pounds 50$.

Over 4 years: $50\times 4=\pounds 200$.

The question also asks for the total amount, so add the interest to the principal: $1000+200=\pounds 1200$.

So the answer is £200 interest, £1200 total. Both parts must be right: multiply by all 4 years, and remember to add the interest on to the £1000 at the end.

With simple interest, each year's interest is worked out on the original £500.

One year's interest: $500\times 0.06=\pounds 30$.

Over 4 years: $30\times 4=\pounds 120$.

The question asks for the total amount, so add this to the deposit: $500+120=\pounds 620$.

The total amount is £620. Watch out for stopping at the interest (£120), for using only one year's interest, and for compounding: $500\times 1.06^4=\pounds 631.24$, which is what a compound account would pay.

With compound interest the balance is multiplied by $1.05$ each year:

After year 1: $200\times 1.05=\pounds 210$.

After year 2: $210\times 1.05=\pounds 220.50$.

The total amount is £220.50, the balance in the account, not the £20.50 of interest on its own. Simple interest would add £10 twice to give exactly £220. The extra 50p is the interest earned on year 1's interest, which is what makes it compound.