Sakira invested £3550 in a savings account for 3 years. She was paid 2.6% per annum compound interest for each of the first 2 years. She was paid R% interest for the third year. Sakira had £3819.21 in her savings account at the end of the 3 years. Work out the value of R. Give your answer correct to 1 decimal place.

GCSE Edexcel Maths Direct & Inverse Proportion: Sakira invested £3550 in a savin

Sakira invested £3550 in a savings account for 3 years - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 2

Question 14

Sakira invested £3550 in a savings account for 3 years. She was paid 2.6% per annum compound interest for each of the first 2 years. She was paid R% interest for th... show full transcript

Worked Solution & Example Answer:Sakira invested £3550 in a savings account for 3 years - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 2

Step 1

Calculate the total amount after 2 years at 2.6% interest

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Answer

To calculate the amount after 2 years of compound interest, use the formula: $A = P(1 + r)^n$ Where:

A = final amount
P = principal amount (£3550)
r = interest rate per year (2.6% = 0.026)
n = number of years (2)

Substituting in the values, we have: $A = 3550(1 + 0.026)^2 = 3550(1.026)^2 \approx 3550(1.052676) \approx 3735.07$ Thus, after 2 years, the total amount in the account is approximately £3735.07.

Step 2

Calculate the amount of interest earned in the third year at R%

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Answer

After 2 years, the amount is £3735.07. To find R%, we first set the final amount after 3 years equal to the total amount received:

Let the interest earned in the third year be: $I_3 = 3735.07 \times \frac{R}{100}$

The final amount is given as £3819.21. Therefore: $3735.07 + I_3 = 3819.21$ This implies: $I_3 = 3819.21 - 3735.07 = 84.14$

Substituting back into our interest formula: $84.14 = 3735.07 \times \frac{R}{100}$

Solving for R gives: $R = \frac{84.14 \times 100}{3735.07} \approx 2.25$ Thus, the value of R is approximately 2.2% when rounded to one decimal place.

Sakira invested £3550 in a savings account for 3 years - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 2

Worked Solution & Example Answer:Sakira invested £3550 in a savings account for 3 years - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 2

Calculate the total amount after 2 years at 2.6% interest

Calculate the amount of interest earned in the third year at R%

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