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 23 - 2018 - Paper 1

Question 23

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 23 - 2018 - Paper 1

Step 1

Calculate the final amount in Northern Savings Bank (NSB) after 8 years using compound interest.

96%

114 rated

Answer

To find the total amount in the NSB account after 8 years with a compound interest rate of 2.5%, we use the formula:

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

Where:

$A$ is the amount of money accumulated after n years, including interest.
$P$ is the principal amount (£6400).
$r$ is the annual interest rate (2.5% = 0.025).
$t$ is the time the money is invested for (8 years).

Thus, we calculate:

$A_{NSB} = 6400(1 + 0.025)^8$ $A_{NSB} = 6400(1.025)^8$ $A_{NSB} = 6400 imes 1.21899 ext{ (approx)}$ $A_{NSB} ext{ (after rounding)} = £7807.18$

Step 2

Calculate the final amount in Central Alliance Bank (CAB) after 8 years using simple interest.

99%

104 rated

Answer

For the CAB account, the simple interest formula is used:

$A = P(1 + rt)$

Where:

$A$ is the total amount of money.
$P$ is the principal amount (£6400).
$r$ is the annual interest rate (2.7% = 0.027).
$t$ is the time the money is invested for (8 years).

Therefore:

$A_{CAB} = 6400(1 + 0.027 imes 8)$ $A_{CAB} = 6400(1 + 0.216)$ $A_{CAB} = 6400 imes 1.216$ $A_{CAB} ext{ (after rounding)} = £7785.44$

Step 3

Calculate the difference in value between the two accounts after 8 years.

96%

101 rated

Answer

Finally, to find the difference between the two final amounts:

$ext{Difference} = A_{NSB} - A_{CAB}$ $ext{Difference} = 7807.18 - 7785.44$ $ext{Difference} = £21.74$

Thus, the difference in value after 8 years is £21.74.

Here are the interest rates for two bank accounts - OCR - GCSE Maths - Question 23 - 2018 - Paper 1

Worked Solution & Example Answer:Here are the interest rates for two bank accounts - OCR - GCSE Maths - Question 23 - 2018 - Paper 1

Calculate the final amount in Northern Savings Bank (NSB) after 8 years using compound interest.

Calculate the final amount in Central Alliance Bank (CAB) after 8 years using simple interest.

Calculate the difference in value between the two accounts after 8 years.

Join the GCSE students using SimpleStudy...