Bank Statements and savings

A bank statement is a record of payments in and out of a bank account. Most people have a current account as it is where their wages, pensions and/or benefits are paid into. The money available in a current account is known as the balance. Payments from a current account can be made by debit card, by direct debit or a standing order.

Payments by a debit card leave the account immediately. This is the usual transaction that takes place when purchasing from a shop or over the internet.

Direct debits are set up with companies who need to take flexible amounts from your account. For example, energy providers offer direct debit payments as the amount that is used each month may vary and they take the required amount at each bill.

Standing orders are similar to a direct debit except that they are for a fixed amount. For example, a standing order would be set up to pay a fixed amount to a charity every month.

Savings

Savings accounts often have a higher rate of interest than current accounts as an incentive to save money with particular financial institutions. However, there are sometimes limits on the amount of withdrawals that can be made so that the bank can hold the money for a longer period.

Example

This table shows the interest rates for two accounts, A and B.

Account AAccount B
Interest: 3.5% per year compound interestInterest: 4% for the first year, 3.5% for the second year and 3% for the third year
No withdrawals until the end of three yearsWithdrawal allowed at any time

Rodney has £5,000 he wants to invest. Which bank would offer the best rate if he wanted to save for 3 years? Why might he not want to use Account A?

Using repeated percentage change methods:

Account A

5,000 \times 1.035^3 = \pounds 5,543.59

Using percentage increase methods:

Account B

5,000 \times 1.04 \times 1.035 \times 1.03 = \pounds 5,543.46

So Account A would give a greater saving by 13 p. However, Rodney may not want to use Account A as the money cannot be accessed for 3 years.

Question

\pounds y was invested for 7 years. It earned compound interest at 2.5% per year. After 7 years the total value of the investment is £9,509.49

How much was the original investment?

Using the repeated percentage change methods the problem can be expressed like this:

y \times 1.025^7 = 9,509.49

To find y divide both sides of this equation by 1.0257.

y = \pounds 8,000