. Margaret is planning to invest up to $22,000 in certificates of deposit at City Bank and People’s Bank. She wants to invest at least $2,000 but no more than $14,000 at City Bank. People’s Bank does not insure more than a $15,000 investment, so she will invest no more than that in People’s Bank. The interest is 6% at City Bank and 6½% at Peoples Bank. This is simple interest for one year. How much should she invest in each bank in order to maximize her income? What is the maximum income?

Question

.  Margaret is planning to invest up to $22,000 in certificates of deposit at City Bank and People’s Bank.  She wants to invest at least $2,000 but no more than $14,000 at City Bank.  People’s Bank does not insure more than a $15,000 investment, so she will invest no more than that in People’s Bank.  The interest is 6% at City Bank and 6½% at Peoples Bank.  This is simple interest for one year.  How much should she invest in each bank in order to maximize her income?  What is the maximum income?

Henry · Answer

Best Investment:

1. Peoples Bank, 15000 @ 6.5 %.

City Bank, 7000 @ 6%.

2. Peoples Bank:
Pt = Po + r*t*Po,
Pt = 15000 + 0.065 / yr *1yr * 15000,
Pt = 15000 + 975 = 15975.

City Bank:
Pt = 7000 + 0.06 / yr * 1yr * 7000,
Pt = 7000 + 420 = 7420.

Total Income = 15975 + 7420 = 23395.