Simple interest

Simple interest is worked out on the amount you started with only, so you earn (or pay) the same amount every year: interest = amount × rate × years. Hire purchase spreads a price over a deposit and payments, and usually costs more than paying cash.

Key facts

  • Simple interest: I = P × r × n (r as a decimal, n in years). The total is P + I.
  • Simple interest is the same every year: find it for one year, then multiply by the number of years.
  • Hire purchase: total paid = deposit + all the instalments. The extra cost is total paid − cash price.

Worked examples

Example 1

£5,000 is invested at 6% simple interest per year for 4 years. How much is it worth at the end?

  1. Interest: 5,000 × 0.06 × 4 = 1,200
  2. Total: 5,000 + 1,200 = 6,200

Answer: £6,200

Example 2

£800 is invested at 3% simple interest per year. How much interest is earned in 5 years?

  1. Find 3% of the amount. 0.03 × 800 = 24
  2. Multiply by the number of years. 24 × 5 = 120

Answer: £120

Example 3

£1,500 is invested at 4% simple interest per year for 3 years. Find the total value.

  1. Find the interest for 3 years. 0.04 × 1,500 × 3 = 180
  2. Add it to the amount. 1,500 + 180 = 1,680

Answer: £1,680

Example 4

How many years does it take £400 to earn £60 at 5% simple interest per year?

  1. Find 5% of the amount: the interest for one year. 0.05 × 400 = 20
  2. Divide the interest wanted by the interest each year. 60 ÷ 20 = 3

Answer: 3 years

Example 5

A TV costs £450 cash. On hire purchase you pay a £90 deposit and 12 payments of £35. How much extra do you pay on hire purchase?

  1. Add the deposit and all the payments. 90 + 12 × 35 = 510
  2. Take away the cash price. 510 − 450 = 60

Answer: £60