# The rate of interest in a bank is 3% pa and the rate of inflation is 4% pa. If a person has the funds in the bank now to buy 20 kg of a fruit, how much fruit in kg could they buy in a year's time...

The rate of interest in a bank is 3% pa and the rate of inflation is 4% pa. If a person has the funds in the bank now to buy 20 kg of a fruit, how much fruit in kg could they buy in a year's time if they leave the money in the bank?

justaguide | Certified Educator

A person can buy 20 kg of fruit right now with the funds available. The rate of inflation is the rate at which the prices increase. As the rate of inflation is 4% per year, if the price of the fruit is X right now, after a year it would be 1.04*X. An amount P deposited in a bank offering a rate of interest p% per year increases to (1+p/100)*P. The rate of interest in the bank is 3% per year. If an amount P is deposited today, the amount after a year would be P*(1.03).

20 kg of fruit can be bought right now. If the price is X, the amount with the person is 20*X. After a year, the person has 20*X*1.03 but the price of fruit is X*1.04.

As a result the number of kilograms of fruit that can be bought is `(20*X*1.03)/(X*1.04)`

= `(20*1.03)/1.04`

`~~ 19.8`

The person can buy approximately 19.8 kg of the fruit after a year.

mathsworkmusic | Certified Educator

If the fruit costs \$X/kg now then 20kg costs \$20X now. Therefore the person has \$20X in the bank now.

In a year's time the fruit will cost \$1.04X/kg (if the inflation rate is 4%).

In a year's time the person's funds in the bank would be worth 1.03 x 20X = \$20.60X (if the interest rate is 3%).

Therefore in a year's time the person would only be able to buy

\$20.60X/(\$1.04/kg) = 19.81kg of fruit

With their available funds, the person would be able to buy only 19.81kg of fruit in a year's time as opposed to 20kg now.

mathsworkmusic | Certified Educator

The inflation of the price of the fruit is 4% so the price increases by 4%.

The interest on the funds is 3% so the funds increase by 3%.

The fruit's value increases to (4-3) = 1% higher than the value of the funds.

Therefore, the person can only buy 99% of the fruit in a year's time that they could buy now. So if they can buy 20kg now, then in a year's time they could only buy 0.99 x 20 = 19.8kg.

Only 19.8kg of fruit could be bought in a year's time.