Question

Olivia and Sadie each take out a loan of £2000 at the same time. The loans have a compound interest rate of 6.5% per year.

2 years after taking out the loan, Olivia pays back & 1000.
3 years after taking out the loan, Sadie pays back £ 1000.
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10 years after taking out the loan, how much more money does Sadie owe than Olivia?
Give your answer in pounds to the nearest 1p.

Answer 1

After 10 years, Sadie owes £21.34 more than Olivia.

Step-by-step explanation:

To find out how much more money Sadie owes than Olivia 10 years after taking out the loan, we need to calculate the total amount owed by each person after 10 years.

Olivia paid back £1000 after 2 years, so she still owes the remaining amount of the loan (£2000 - £1000 = £1000) after 2 years.

Using compound interest formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate that Olivia owes

£1000 * (1 + 0.065/1)^(1 * 8) = £1729.07 after 10 years.

Sadie paid back £1000 after 3 years, so she still owes the remaining amount of the loan

(£2000 - £1000 = £1000) after 3 years.

Using the same formula, we can calculate that Sadie owes

£1000 * (1 + 0.065/1)^(1 * 7) = £1707.73 after 10 years.

Therefore, Sadie owes

£1729.07 - £1707.73 = £21.34 more than Olivia after 10 years.