Example – two methods
A Lady put £400 in a savings account for 3 years at 5%. What will she have at the end of 3 years?
You have two ways of completing this.
Let’s not use a formula let’s just use logic
End of 1st year `=£400=100%`
(See percentages for this method)
End of 1st year -
End of 2nd year
End of 3rd year
The lady would have £463.05 at the end of the 3rd year
Use the formula
The lady will have £463.05 at the end of 3 years.
Example - Interest per year
A woman invests £2000 in a savings account and this account pays 6% interest per year. How much will she have in the account after nine years to the nearest pound?
After nine years the woman will have £3,379 to the nearest pound in the savings account.
Example - Interest per month
If you invest £1,000 earning 5% compound monthly.
How much will you have after 15 years to the nearest pound?
See how to calculate powers on next page
After 15 years you will have £2,114 to the nearest pound (of this amount £1,000.00 is your initial investment).
Example - Depreciation (Negative interest)
A car cost £8,000 but it depreciates by 9% each year. How much is it worth after 4 years?
The annual interest formula works in exactly the same way
The minus on the interest rate r.
After 4 years the car is only worth £5,486.00
Example - Interest rate quarterly
A lady invests £5,000 in a savings account which compounds the interest quarterly (i.e. 4 times a year), after 5 years how much will the lady have in the account if the interest rate is 8% per year.
The lady will have £7,429.74 at the end of five years.
If this had been compound interest yearly then the answer would have been £7,346.64
Example - Not just for money
A bacteria colony multiplies at the rate of 15% per day. If the colony started with 800 bacteria cells. How many cells would be in the bacteria colony at the end of one week?
Normally t = time is over a year but the period of growth is per day so in this case t = 1 for one day
`n=` once per day too.
Note the minus on the interest rate r.
There will be 2,128 bacteria cells after one week.
Example – Finding the principal sum
An investment account with a 10% yearly compound interest rate contains £331 at the end of 3 years. What was the initial investment?
The initial investment or starting amount was £248.69