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%.