A company invests a total of $40 comma 000 of surplus funds at two annual rates of interest: 5 % and 6one half %. It wishes an annual yield of no less than 6one fourth %. What is the least amount of money that the company must invest at the 6one half % rate? The company should invest at least $ nothing at 6one half %.

Question

Mathematics

Darrell Boyd

19 August, 12:07

A company invests a total of $40 comma 000 of surplus funds at two annual rates of interest: 5 % and 6one half %. It wishes an annual yield of no less than 6one fourth %. What is the least amount of money that the company must invest at the 6one half % rate? The company should invest at least $ nothing at 6one half %.

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Gracie Gross · Answer 1

Suppose the company invests x of their surplus in the 5% rate (and thus 40000-x has 6.5%). Then we have that 5%*x + (40000-x) 6.5%=6.25%*40000.

We have that solving this, 5% * x+40000*6.5%-6.5%*x = 6.25% * 40000 Accumulating terms, 1.5%*x=0.25%*40000 x=40000/6 = 6666.67$. We see that if we invest 6666.67$ at 5%, we get exactly the given rate. If we invest more, we obviously get less. Hence, we have that the company has to invest at 6.5% more than 40000-6666.67=33333.33$