Here are the interest rates for two bank accounts. Northern Savings Bank (NSB) 2.5% per year compound interest Central Alliance Bank (CAB) 2.7% per year simple interest Mia puts £6400 in each account. Calculate the difference in value between the two accounts after 8 years. Give your answer correct to the nearest penny:

GCSE OCR Maths Percentages: Here are the interest rates for

Here are the interest rates for two bank accounts - OCR - GCSE Maths - Question 4 - 2018 - Paper 4

Question 4

Here are the interest rates for two bank accounts. Northern Savings Bank (NSB) 2.5% per year compound interest Central Alliance Bank (CAB) 2.7% per year simple int... show full transcript

Worked Solution & Example Answer:Here are the interest rates for two bank accounts - OCR - GCSE Maths - Question 4 - 2018 - Paper 4

Step 1

Calculate the value in Northern Savings Bank (NSB) after 8 years

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Answer

The formula for compound interest is:

$A = P(1 + r)^n$

Where:

$A$ is the amount of money accumulated after n years, including interest.
$P$ is the principal amount (the initial amount of money).
$r$ is the annual interest rate (decimal).
$n$ is the number of years.

For NSB:

$P = £6400$
$r = 0.025$ (2.5% as a decimal)
$n = 8$

Substituting these values into the formula:

$A = 6400(1 + 0.025)^8$ $A = 6400(1.025)^8$ $A \approx 6400 \times 1.2184 \approx £7807.06$

Step 2

Calculate the value in Central Alliance Bank (CAB) after 8 years

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Answer

The formula for simple interest is:

$A = P(1 + rt)$

Where:

$A$ is the total amount after time t,
$P$ is the principal amount,
$r$ is the annual interest rate,
$t$ is the time in years.

For CAB:

$P = £6400$
$r = 0.027$ (2.7% as a decimal)
$t = 8$

Substituting these values into the formula:

$A = 6400(1 + 0.027 \times 8)$ $A = 6400(1 + 0.216)$ $A = 6400 \times 1.216 \approx £7782.40$

Step 3

Calculate the difference in value between the two accounts

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Answer

Now, to find the difference between the two amounts:

Difference = Value in NSB - Value in CAB

$Difference \approx 7807.06 - 7782.40 \approx £24.66$

Therefore, the difference in value between the two accounts after 8 years is approximately £24.66.

Here are the interest rates for two bank accounts - OCR - GCSE Maths - Question 4 - 2018 - Paper 4

Worked Solution & Example Answer:Here are the interest rates for two bank accounts - OCR - GCSE Maths - Question 4 - 2018 - Paper 4

Calculate the value in Northern Savings Bank (NSB) after 8 years

Calculate the value in Central Alliance Bank (CAB) after 8 years

Calculate the difference in value between the two accounts

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