Question

2. (20 points) Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 3%, one paying 5.5%, and one paying 9% simple interest per year. Cyndee wants to put twice as much in the lowest-yielding (least risky) account as in the highest-yielding account. How much should she invest in each account to achieve a total annual return of $2540.

Answer 1

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Let money invested at 3% :x " " . .. 5.5"), y 91. z :: Total money = 50,000 1. +y+z= 50,000 — O Money in lowest yielding is twice as much as in highest yielding 20-22 7-227-0 — Total annual return =2540 ..3722+5.5%+97.7=2540 3x+ 5.5y+92= 254000 - 3 solving equations , & ③ by Gaussian ' ' ' | 50,000 1 0 - 20 3 515 9/254000] R₂ R₂-IR, li 50000] R33 R3-3R, Jo-1 -3 -50000 lo 215 T . 6 104000 R2 R24 lei 50000] 3 50000 lo 205 6 10,4000) Rio Ri-R2 ru o -zlo) - R3 R3-2-5R2 to 1.3 150000 lo 0 -105 21000 Ry -> R3761.5) [i 0 -21.07 0 1 3 / 50 000 lo O 14000) Rio Ri+2 R3 lio o 128000] R2 R₂-3R3 Loiol 8000 lo O 14000 Least risky a = $28000 Intermediate y = $8000 Highest yielding 2= $14000