A financial officer is splitting P500,000 between two bonds,one paying 6% interest and the other paying 8% interest(this bond carries more risk).A minimum of P36,500 of interest payments per year is required.How much can she spend on the 6%?
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Let 'd' be amount invested at 6%. Therefore there is 500,000-d invested at 8%
This will find minimum invested at 6%.
6% of d plus 8% of 500,000-d equals 36,500
0.06d + 0.08(500,000-d) = 36,500
0.06d + 40,000-0.08d = 36,500
-0.02d + 40,000 = 36,500
add 0.02d to both sides of equation
40,000 = 36,500 + 0.02d
subtract 36,500 from both sides
40,000 - 36,500 = 0.02d
3,500 = 0.02d
divide both sides by 0.02
175,000 = d
To earn a minimum of 36,500 she must put 175,000 into the 6% and the balance in the 8% (325,000)
This will find minimum invested at 6%.
6% of d plus 8% of 500,000-d equals 36,500
0.06d + 0.08(500,000-d) = 36,500
0.06d + 40,000-0.08d = 36,500
-0.02d + 40,000 = 36,500
add 0.02d to both sides of equation
40,000 = 36,500 + 0.02d
subtract 36,500 from both sides
40,000 - 36,500 = 0.02d
3,500 = 0.02d
divide both sides by 0.02
175,000 = d
To earn a minimum of 36,500 she must put 175,000 into the 6% and the balance in the 8% (325,000)