Question

Samir started a four-year course at university in 2016

On 1 September 2020 he started a job on an annual salary of £36 000
On that day he owed £23 700 to the Student Loan Company.
He knows that
interest on his student loan is charged at the RPI + 1%
he will receive a pay rise of £1000 after one year of work
the threshold for student loans will stay the same.
Work out how much he will owe on 1 September 2022
Assume that
interest is added to the loan annually on 31 August after the full year of repayments has
been deducted
and
the RPI stays the same for the two years.

Answer 1

To solve this problem, we need to calculate the interest accrued over the two-year period and then add it to the initial loan amount.

The formula to calculate the interest after one year is:

Interest = Initial loan amount * (1 + (RPI + 1%) / 100)

Given:

Initial loan amount = £23,700

RPI + 1% = x (let's assume a value for simplicity)

Now, we are asked to calculate how much he will owe on 1 September 2022 after receiving a pay rise a year later.

After the first year of work, Samir's salary is £36,000 + £1,000 = £37,000.

We need to calculate the interest for the first year:

Interest1 = £23,700 * (1 + x/100)

So, the amount owed on 1 September 2021 will be:

Amount owed1 = £23,700 + Interest1

The RPI stays the same for the two years, so we can assume the same value of x for the second year.

At the end of the second year (on 31 August 2022), another year's interest is added. The salary for the second year is £37,000.

Interest2 = Amount owed1 * (1 + x/100)

So, the amount owed on 1 September 2022 will be:

Amount owed2 = Amount owed1 + Interest2

With this information, you can calculate the amount owed on 1 September 2022. Simply substitute the values for Interest1 and Interest2 back into the equations for Amount owed1 and Amount owed2.