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3 Charlie invests £4000 for 3 years in a savings

account.
She gets 2% per annum compound interest in
the first year, then x% for 2 years.
Charlie has £4228.20 at the end of 3 years,
work out the value of x.

User Barn
by
7.9k points

1 Answer

1 vote

Answer: The value of x is 3.45%

Explanation:

We can solve the problem by using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = final amount

P = principal (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time in years

In the first year, Charlie gets 2% interest, compounded annually. So, using the formula, we have:

A1 = 4000(1 + 0.02/1)^(1*1)

A1 = 4080

After the first year, Charlie has £4080 in her account. For the next two years, she gets x% interest, compounded annually. Using the formula again, we have:

A2 = 4080(1 + x/100/1)^(1*2)

A2 = 4080(1 + x/100)^2

Finally, after three years, Charlie has £4228.20 in her account. So, we can set up an equation:

A1 * A2 = 4000 * (1 + 0.02) * 4228.20

Substituting the values of A1 and A2, we get:

4080(1 + x/100)^2 = 4366.4496

Dividing both sides by 4080, we get:

(1 + x/100)^2 = 1.0694

Taking the square root of both sides, we get:

1 + x/100 = 1.0345

Subtracting 1 from both sides and multiplying by 100, we get:

x = 3.45

Therefore, the value of x is 3.45%.

User Broly
by
8.2k points
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