Betsy, a recent retiree, requires $6000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 13 % per year or in a certificate of deposit (CD) paying 5 % per year. How much money should be invested in each to realize exactly $6,000 in interest per year?

Total funds available with Betsy = $50,000

Interest rate in B-rated bonds = 13% per year

Let amount invested in B-rated bonds be x

Interest rate in certificate of deposit (CD) = 5 % per year

Amount invested in CD = 50,000-x

Now, we have to determine x such that Betsy can get exactly $6,000 in interest per year. Hence:

x * 13% + (50,000 - x) * 5% = 6,000

⇒ 0.13x - 0.05x + 2,500 = 6,000

⇒ 0.08x = 3,500

⇒ x = 43,750

Hence, Betsy should invest $43,750 in B-rates bonds

And 50,000 - x = 50,000 - 43,750 = 6,250

And she should invest 6,250 in CD