Question

Briony invests some money. Interest is paid on the money at a rate of 2% per annum for the first year and 1% per annum for the second year. After two years, the investment is worth £8653.68 How much did Briony invest?

Answer 1

Brionny invested £8400.

Explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

`E = P*I*t`

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

`T = E + P`

In this question:

We divide in two intervals, the first year and the second year. We have to know that the amount after the end of the first year is the principal at the start of the second year.

First year:

Amount of 2% interest, during 1 year.

So the interest earned is:

`E = P*I*t = P*0.02*1 = 0.02P`

The total amount at the end of the first year is:

`T = E + P = 0.02P + P = 1.02P`

Second year:

We have that:

`P = 1.02P`

The interest earned is of:

`E = P*I*t = 1.02P*0.01*1 = 0.0102P`

The total amount is:

`T = E + P = 0.0102P + 1.02P = 1.0302P`

After two years, the investment is worth £8653.68 How much did Briony invest?

So

`1.0302P = 8653.68`

`P = (8653.68)/(1.0302)`

`P = 8400`

Brionny invested £8400.