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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. 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.​

User Neverlastn
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1 Answer

3 votes

Answer:

£0

Explanation:

To calculate the outstanding loan balance for each person after 10 years, we can use the following formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial loan amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

For Olivia, we can calculate her outstanding balance after 10 years as follows:

P = £2000

r = 6.5% per year = 0.065

n = 1 (compounded annually)

t = 10 years

A = £2000(1 + 0.065/1)^(1*10) = £3829.71

After paying back £1000, Olivia's outstanding balance would be £2829.71.

For Sadie, we can calculate her outstanding balance after 10 years as follows:

P = £2000

r = 6.5% per year = 0.065

n = 1 (compounded annually)

t = 10 years

A = £2000(1 + 0.065/1)^(1*10) = £3829.71

After paying back £1000, Sadie's outstanding balance would be £2829.71.

To find the difference between Sadie's outstanding balance and Olivia's outstanding balance, we can subtract Olivia's balance from Sadie's balance:

£2829.71 - £2829.71 = £0

Therefore, Sadie does not owe more money than Olivia after 10 years, as both of their outstanding balances are the same at that point in time.

This text describes a scenario where two individuals, Olivia and Sadie, take out a loan of £2000 each at the same time. The loans have a compound interest rate of 6.5% per year. Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods.

Two years after taking out the loan, Olivia pays back £1000, which reduces her outstanding loan balance to £2000 plus accumulated interest. Three years after taking out the loan, Sadie pays back £1000, which also reduces her outstanding loan balance to £2000 plus accumulated interest.

The question asks how much more money Sadie owes than Olivia 10 years after taking out the loan. To solve this problem, we need to calculate the outstanding loan balance for both Olivia and Sadie after 10 years, using the compound interest formula. We can then subtract Olivia's outstanding balance from Sadie's outstanding balance to find the difference.

It's worth noting that the question specifies that the answer should be given in pounds to the nearest 1p, which means we need to round our final answer to the nearest penny.

User Hamed Hamedi
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