Nick invested £8,500 in a savings account with an annual interest rate of R%. The interest earned in one year can be expressed as R/100×8500, and after paying tax at a rate of 30%, the amount Nick receives is (1−0.3) times the interest. This can be represented as 0.7×R/100×8500.
Setting up the equation 0.7×R/100×8500=166.60, we solve for R. First, we simplify the expression and then isolate R:
R/100×8500=0.7166.60
By multiplying both sides by 100/8500, we find:
R=166.60×100/0.7×8500
After computation, R≈23800/595, which simplifies to approximately 40%.
In conclusion, the interest rate R is approximately 40%. This means that Nick's investment of £8,500 in the savings account yields an annual interest of 40%, and after accounting for a 30% tax on the interest, he receives £166.60. This illustrates the interplay between the interest rate, initial investment, and tax considerations in determining the final return on an investment. Nick's savings account, with an approximate interest rate of 40%, results in £166.60 after one year, factoring in both the initial investment and a 30% tax on the earned interest.