Simple interest over a fraction of a year
If money is not left in a bank account for a whole year then only a fraction of the interest gets paid.
Example
Find the interest that Damon earns on \(\pounds40\) if he keeps it in the bank, paying \(8.5\%\) interest per annum, for six months.
Interest for one year \( = 8.5\%\,of\,\pounds40\)
\(= \frac{{8.5}}{{100}} \times 40\)
\(= \pounds3.40\)
Interest for six months = \(\frac{1}{2}\,of\,\pounds3.40\)
\(= \pounds1.70\)
New balance:
\(= 40 + 1.70\)
\(= \pounds41.70\)
Damon will earn \(\pounds1.70\) in interest.
Now try this question:
Question
Eliza has \(\pounds560\). She deposits it in a bank account that pays \(3.7\%\) interest per annum.
She leaves it in the bank for two months.
How much money does Eliza have now?
Interest for one year \(= 3.7\%\,of\,\pounds560\)
\(=\frac{3.7}{100} \times 560\)
\(= \pounds20.72\)
Interest for two months = \(\frac{1}{6}\) of \(\pounds20.72\)
\(= \pounds3.45\) (rounding down to the nearest pence)
New balance:
\(= 560 + 3.45\)
\(= \pounds563.45\)
After two months Eliza has \(\pounds563.45\).