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 Proportion: 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 using compound interest

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Answer

To calculate the total amount in the NSB account after 8 years with compound interest, we use the formula:

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

where:

$P$ = initial principal (£6400)
$r$ = annual interest rate (2.5% = 0.025)
$n$ = number of years (8)

Plugging in the values:

$A = 6400(1 + 0.025)^8$ $A = 6400(1.025)^8$ Using a calculator, we find: $A = 6400 imes 1.2184 = 7800.77$ The amount after 8 years in NSB will be approximately £7800.77.

Step 2

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

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Answer

For the CAB account, we use the simple interest formula:

$A = P + (P imes r imes t)$

where:

$P$ = initial principal (£6400)
$r$ = annual interest rate (2.7% = 0.027)
$t$ = number of years (8)

Calculating the interest earned:

$Interest = P imes r imes t = 6400 imes 0.027 imes 8 = 1385.76$

Now, we calculate the total amount:

$A = 6400 + 1385.76 = 7785.76$ The amount after 8 years in CAB will be approximately £7785.76.

Step 3

Calculate the difference between the two accounts

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Answer

To find the difference between the amounts in the two accounts, we subtract the total in CAB from the total in NSB:

Difference = £7800.77 - £7785.76 = £15.01.

Thus, the difference in value between the two accounts after 8 years is approximately £15.01.

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 using compound interest

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

Calculate the difference between the two accounts

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