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An inheritance of $25,000 is divided among three investments yielding a total of$1275 in interest per year. The interest rates for the three investments are 4.5%, 5%, and 8%. The amounts invested at 5% and 8% are $4000 and$10,000 less than the amount invested at 4.5%, respectively. Find the amount invested at each rate.
Solution
VerifiedLet be the amount invested at 4.5%, be the amount invested at 5%, and be the amount invested at 8%.
The total investment is so .
dollars invested at 4.5% earns dollars in interest, dollars invested at 5% earns dollars in interest, and dollars invested at 8% earns dollars in interest. The total amount of interest earned on the three investments is then dollars. Since the total interest earned is , then .
If the amount invested at 5% is less than the amount invested at 4.5%, then .
If the amount invested at 8% is less than the amount invested at 4.5%, then .
The system of equations is then
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