Louise invests £x in Better Investments for 3 years. Sadiq invests £x in County Bank for 3 years. Better Investments: Compound Interest 2.5% per annum County Bank: Compound Interest 2% per annum for the first two years 3.5% per annum for each extra year At the end of the 3 years, the value of Louise’s investment is £344,605. Work out the value of Sadiq’s investment at the end of the 3 years.

GCSE Edexcel Maths Coordinate Geometry: Louise invests £x in Better Inve

Louise invests £x in Better Investments for 3 years - Edexcel - GCSE Maths - Question 11 - 2021 - Paper 2

Question 11

Louise invests £x in Better Investments for 3 years. Sadiq invests £x in County Bank for 3 years. Better Investments: Compound Interest 2.5% per annum County Bank:... show full transcript

Worked Solution & Example Answer:Louise invests £x in Better Investments for 3 years - Edexcel - GCSE Maths - Question 11 - 2021 - Paper 2

Step 1

Work out the initial investment for Louise

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Answer

To find the initial investment, we need to start by setting up the equation for compound interest:

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

Where:

A = the amount after time n
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of years

For Louise:

A = £344,605
r = 0.025 (2.5% as a decimal)
n = 3

Substituting these values into the formula:

$344,605 = P(1 + 0.025)^3$

Calculating the right-hand side:

$1.025^3 = 1.076890625$

So the equation becomes:

$344,605 = P(1.076890625)$

Now, solving for P:

$P = \frac{344,605}{1.076890625} = 319,078.54$

Thus, the initial investment for Louise was approximately £319,078.54.

Step 2

Calculate the value of Sadiq’s investment

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Answer

Sadiq's investment also goes through compound interest, but at different rates:

For the first 2 years at 2%, and for the 3rd year at 3.5%.

First two years compound growth: The formula for the first two years is:

$A = P(1 + 0.02)^2$

For the third year: We take the amount from the end of the second year and compound it at 3.5% for one more year:

$A = A_{end ext{ of year 2}}(1 + 0.035)$

Now, substituting the initial amount P which we already found for Louise:

Substituting into the equations:

After first two years:

$A_{end ext{ of year 2}} = 319,078.54(1 + 0.02)^2 = 319,078.54(1.0404) = 331,998.22$

For the third year:

$A_{end ext{ of year 3}} = 331,998.22(1 + 0.035) = 331,998.22(1.035) = 343,114.38$

Therefore, the value of Sadiq’s investment at the end of 3 years is approximately £343,114.38.

Louise invests £x in Better Investments for 3 years - Edexcel - GCSE Maths - Question 11 - 2021 - Paper 2

Worked Solution & Example Answer:Louise invests £x in Better Investments for 3 years - Edexcel - GCSE Maths - Question 11 - 2021 - Paper 2

Work out the initial investment for Louise

Calculate the value of Sadiq’s investment

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