Question 6A sum invested in a fixed interest bank deposit account increased in value by 40% over 5 years.Question 6Which of the following is closest to the fixed rate of interest over that period, assuming that each year the interest was reinvested in the deposit account?5%6%7%8%
Question
Question 6A sum invested in a fixed interest bank deposit account increased in value by 40% over 5 years.Question 6Which of the following is closest to the fixed rate of interest over that period, assuming that each year the interest was reinvested in the deposit account?5%6%7%8%
Solution
To solve this problem, we need to find the annual interest rate that would result in a 40% increase over 5 years. We can use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
where: A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for in years.
In this case, we know that the principal amount (P) increased by 40% over 5 years, so A = 1.40P. The interest is compounded annually, so n = 1. We're solving for r, the annual interest rate.
1.40P = P(1 + r/1)^(1*5)
Solving for r gives us:
1.40 = (1 + r)^5
Taking the fifth root of both sides:
1.0807 = 1 + r
Subtracting 1 from both sides:
r = 0.0807
Converting this to a percentage gives us an annual interest rate of approximately 8.07%.
So, the closest answer to the fixed rate of interest over that period is 8%.
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