Question

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​%.

Answer 1

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%.