# Annuity, Linear programming problem

3. A man has amassed $1.5 million for his retirement. It is an account earning interest at an annual rate of 7.32%, with monthly compounding. He decides to pay himself equal amounts at the end of every month for 20 years, depleting the entire original amount. How much is each monthly payment?

6. A nutritionist is planning evening meals at a convalescent facility using foods I, II, and III. She wishes to make each meal cost as little as possible while still satisfying certain restrictions.

Each meal must contain at least 200 mg of Vitamin C, 300 mg of Calcium, and 0.05 grams of Fiber, and costs 15 cents. Each ounce of food II contains 50 mg of Vitamin C, 90 mg of calcium, and 1.25 grams of fiber, and costs 20 cents. Each ounce of food III contains 80 mg of Vitamin C, 85 mg of calcium, and 1.65 grams of fiber, and costs 28 cents. Because of details in a contract with the food supplier, a minimum order of 1 ounce of food II per meal is also required.

Formulate, but ***DO NOT SOLVE***, the appropriate linear programming problem.

Note: Food I is a typo. I guess it's just Foods II and III

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#### Solution Preview

3. A man has amassed $1.5 million for his retirement. It is an account earning interest at an annual rate of 7.32%, with monthly compounding. He decides to pay himself equal amounts at the end of every month for 20 years, depleting the entire original amount. How much is each monthly payment?

Annual interest rate = 7.32%

Therefore monthly interest rate= 7.32%/12 = 0.61%

Frequency= M Monthly

No of years= 20

No of Periods= 240 months

Discount rate annually= 7.32% annual

Discount rate per period= 0.6100% Monthly

n= 240

r= 0.61%

PVIFA (240 periods, .61% rate ) = 125.8459

Each monthly payment=

Present Value= $1,500,000

Each monthly payment= $11,919 ...

#### Solution Summary

Calculates annuity and sets up a linear programming problem