A company invests a total of $40 comma 00040,000 of surplus funds at two annual rates of interest: 55% and 66one half 1 2%.
It wishes an annual yield of no less than 6one fourth 1 4%. What is the least amount of money that the company must invest at the 66one half 1 2% rate? The company should invest at least how much money at 66one half 1 2%.
The only way this problem makes sense is if we are investing $40,000 at either 5% and 6.5%, and we want an annual yield of at least 6.25%. Then we can let x be the amount invested at 6.5%, and (40,000 - x) be the amount invested at 5%. x(0.065) + (40,000 - x)(0.05) = (40,000)(0.0625) 2,000 + 0.015x = 2500 0.015x = 500 x = 33,333 Therefore, the company must invest at least $33,333 at 6.5% to get an annual yield of at least 6.25%.
