Ykay, this is the solution:
Let x to represent the amount invested in the account that pays 2.9% simple interest, therefore 9,500 - x would be the amount invested in the account that pays 1.9% simple interest.
The time of the investment is 1 year or 12 months.
Now, let's recall the formula of the simple interest:
A = P * (1 + rt), where:
A = Final amount
P = Initial principal balance
r = Annual interest rate
t = Time in years
For our case, A would be:
9,500 + 260.50
9,760.50
rate 1 = 2.9% = 0.029
rate 2 = 1.9 = 0.019
In consequence, our equation to solve for x is:
x (1 + 0.029 * 1) + (9,500 - x) (1 + 0.019 * 1) = 9,760.50
1.029x + (9,500 - x) (1.019) = 9,760.50
1.029x + 9,680.50 - 1.019x = 9,760.50
0.01x = 9,760.50 - 9,680.50
0.01x = 80
Multiplying by 100 at both sides:
0.01x * 100 = 80 * 100
x = 8,000
9,500 - x = 9,500 - 8,000 = 1,500
Thus, Angelo invested:
• $ 8,000 in the account that pays 2.9% simple interest ($ 232 of interest)
,
• $ 1,500 in the account that pays 1.9% simple interest ($ 28.50 of interest)