Anil wants to invest £25,000 for 3 years in a bank. Personal Bank Compound Interest 2% for each year Secure Bank Compound Interest 4.3% for the first year 0.9% for each extra year Which bank will give Anil the most interest at the end of 3 years? You must show all your working.

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Anil wants to invest £25,000 for 3 years in a bank - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 2

Question 6

Anil wants to invest £25,000 for 3 years in a bank. Personal Bank Compound Interest 2% for each year Secure Bank Compound Interest 4.3% for the first year 0.9% for... show full transcript

Worked Solution & Example Answer:Anil wants to invest £25,000 for 3 years in a bank - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 2

Step 1

Calculate interest using Personal Bank

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Answer

To calculate the total amount after 3 years with the Personal Bank, we first need to determine the compound interest formula:

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

Where:

$A$ is the total amount after time $n$ ,
$P$ is the principal amount (£25,000),
$r$ is the annual interest rate (2% or 0.02), and
$n$ is the number of years (3).

Plugging in the values:

$A = 25000(1 + 0.02)^3$

Calculating:

$A = 25000(1.02)^3 = 25000(1.061208) \approx 26530.20$

The total amount from the Personal Bank after 3 years will be approximately £26,530.20.

Step 2

Calculate interest using Secure Bank

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Answer

For the Secure Bank, the interest calculation must account for different rates:

For the first year, at 4.3%, the total amount will be:

$A_1 = 25000(1 + 0.043) = 25000(1.043) = 26075$

For the second year, applying the 0.9% rate:

$A_2 = 26075(1 + 0.009) = 26075(1.009) \approx 26338.68$

For the third year, again applying 0.9%:

$A_3 = 26338.68(1 + 0.009) = 26338.68(1.009) \approx 26603.67$

Thus, the total amount from the Secure Bank after 3 years will be approximately £26,603.67.

Step 3

Conclusion

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Answer

Comparing the two outcomes:

Personal Bank: £26,530.20
Secure Bank: £26,603.67

The Secure Bank will provide more interest, totalling approximately £26,603.67.

Anil wants to invest £25,000 for 3 years in a bank - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 2

Worked Solution & Example Answer:Anil wants to invest £25,000 for 3 years in a bank - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 2

Calculate interest using Personal Bank

Calculate interest using Secure Bank

Conclusion

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