Answer:
Explanation:
To solve the problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the principal amount (the initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time in years
We can use this formula for each of the two years and then add the results to find the final amount.
For the first year, we know that the principal (P) is £12000, the time (t) is 1 year, and the final amount (A) is £12336. We do not know the interest rate (r) or the compounding frequency (n), but we can solve for them using the given information.
Using the formula, we have:
£12336 = £12000(1 + r/n)^(n*1)
Dividing both sides by £12000, we get:
1.028 = (1 + r/n)^n
Taking the natural logarithm of both sides, we get:
ln(1.028) = n*ln(1 + r/n)
Solving for n, we get:
n = ln(1.028) / ln(1 + r/n)
For the second year, we know that the principal (P) is £12336 (the final amount from the first year), the time (t) is 1 year, the interest rate (r) is x/2%, and the compounding frequency (n) is the value we just calculated.
Using the formula, we have:
A = £12336(1 + (x/2)/n)^(n*1)
Substituting the value we calculated for n, we get:
A = £12336(1 + (x/2)/ln(1.028))^(ln(1.028)*1)
Simplifying, we get:
A = £12336(1 + (x/2)/ln(1.028))^ln(1.028)
So the value of Jean's investment at the end of 2 years is the result of compounding the interest earned in the first year and second year, which is:
Final amount = £12336(1 + (x/2)/ln(1.028))^ln(1.028) * (1 + x/200)
Note that we use the annual interest rate of x/2% in the second year, but we need to express it as a decimal by dividing by 100. Similarly, we use x/200 instead of x/100 to express the interest rate over the 2-year period.