Final answer:
The total investment across the three accounts with interest rates of 5%, 7%, and 8% that yields $780 in annual interest is $11,700.
Step-by-step explanation:
The total annual interest from investments at 5%, 7%, and 8% is $780. Since equal amounts are invested at each rate, let's denote the common amount of investment as 'x'. We can set up an equation to find the total investment by expressing the annual interest for each investment and then adding them to equal $780.
The equations are as follows:
- Interest from investment at 5%: 0.05x
- Interest from investment at 7%: 0.07x
- Interest from investment at 8%: 0.08x
Adding these together, we get the total annual interest:
0.05x + 0.07x + 0.08x = $780
Combining like terms, that’s:
0.20x = $780
Solving for 'x', we divide both sides by 0.20:
x = $780 / 0.20
x = $3900
Therefore, the amount invested at each rate is $3900, and the total investment is 3 times $3900, which is $11700.