An investment adviser invested 100000 in two accounts one in

An investment adviser invested $100,000 in two accounts. one investment earned 4% simple interest, and the other investment earned 7.5% annual simple interest. The amount of interest earned for 1 year was $6800. How much was invested in each account? $18,000 @82,000 @ 7.5 % $20,000 @ 4% $30,000 @ 7.5% $64,000 @4% $36,000 @7.5%. $32,000 @ 4 % $68,000 @7.5% $12,000 @ 4% $88,000 @ 7.5 %

Solution

Let $ x be invested in the account earning 7.5 % simple interest. Then the amount invested in the account earning 4 % simple interest is 100000-x. The interest on $ x at 7.5 % simple interest for an year is x*7.5/100 = 0.075x and the interest on $ 10000 -x at 4 % simple interest for an year is (100000-x)*4/100 = 4000 – 0.04x. Therefore, 0.075x + 4000- 0.04x = 6800 or, 0.075x - 0.04x = 6800-4000 or, 0.035x = 2800 so that x = 2800/0.035 = 80000. Then 100000-x = 100000-80000 = 20000. Thus, $ 80000 were invested in the account earning 7.5 % simple interest and $ 20000 invested in the account earning 4 % simple interest.