Question

On 1st January 2016 Beth invested some money in a bank account.The account pays 2.5% compound interest per year.On 1st January 2017 Beth withdrew £1000 from the account.On 1st January 2020 she had £17,466 in the account.Work out how much money Beth originally invested in the account.

Answer 1

Beth originally invested approximately £15,356.14 in the bank account.

Step-by-step explanation:

To solve this problem, we need to use the compound interest formula. The formula is given by:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount
• P is the principal (initial investment)
• r is the annual interest rate (as a decimal)
• n is the number of times that interest is compounded per year
• t is the number of years

In this case, Beth had £17,466 after 4 years, so we can plug in the values into the formula and solve for the principal:

17,466 = P(1 + 0.025/1)^(1*4)

17,466 = P(1.025)^4

Divide both sides of the equation by (1.025)^4:

P = 17,466 / (1.025)^4

Using a calculator, we get:

P ≈ £15,356.14