Gwen invested 2100 pounds for three
years in a savings account, which pays compound interest. The interest rate for the first two
years was five percent. The interest rate for the third
year was 1.5 percent. How much did Gwen have in her
savings account at the end of the three-year period?
Interest is money that a bank pays
to you in return for investing your money with them. Compound interest means that each
year the interest you received isn’t just calculated on your initial investment, but
also on interest that you’ve already had paid into the account. In each of the first two years,
Gwen will be paid five percent of the amount that’s in her account at the start of
the year as interest. Assuming she doesn’t make any
withdrawals, she’ll also have 100 percent of the amount she started with, which
means in total she’ll have 105 percent of the amount of money that was in her
account at the beginning of the year.
In order to find 105 percent of a
number, we first convert this to a decimal by dividing by 100, giving 1.05. We can then multiply a number by
this in order to find 105 percent of it. In the third year, the interest
rate is lower. It’s only 1.5 percent, which means
Gwen will have 101.5 percent of her money. The decimal multiplier for the
third year then is 1.015.
To work out how much Gwen has in
her account at the end of the three-year period, we take her starting investment of
2100 pounds multiply it by 1.05 to find what she has at the end of the first year
multiply it by 1.05 again to find what she has at the end of the second year and
then multiply it by 1.015 to find what she has at the end of the third year. We could replace 1.05 multiplied by
1.05 with 1.05 squared.
Typing this into our calculator, we
get 2349.97875. Now, as this represents an amount
of money, we need to round our answer to two decimal places, which is to the nearest
penny. The amount of money Gwen has in her
savings account at the end of the three-year period to the nearest penny is 2349
pounds and 98 pence.