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Sagot :
Using simple interest, it is found that:
- $10,500 was invested at 2%.
- $39,000 was invested at 4%.
Simple Interest
Simple interest is used when there is a single compounding per time period.
The interest after t years in is modeled by:
[tex]I(t) = Prt[/tex]
In which:
- P is the initial amount.
- r is the interest rate, as a decimal.
In this problem, considering that there are two investments:
- A total of $49,500 was invested, hence [tex]P_1 + P_2 = 49500[/tex].
- One investment yields 2% and the other yields 4%, hence the rates are [tex]r_1 = 0.02, r_2 = 0.04[/tex].
- The annual income is of $1770, hence [tex]t = 1, I_1 + I_2 = 1770[/tex].
Considering the rates, we have that:
[tex]I_1 = 0.02P_1[/tex]
[tex]I_2 = 0.04P_2[/tex]
Considering that [tex]I_1 + I_2 = 1770 \rightarrow I_2 = 1770 - I_1[/tex]:
[tex]I_1 = 0.02P_1[/tex]
[tex]1770 - I_1 = 0.04P_2[/tex]
Adding the equations:
[tex]0.02P_1 + 0.04P_2 = 1770[/tex]
Considering that [tex]P_1 + P_2 = 49500 \rightarrow P_2 = 49500 - P_1[/tex], we have that:
[tex]0.02P_1 + 0.04P_2 = 1770[/tex]
[tex]0.02P_1 + 0.04(49500 - P_1) = 1770[/tex]
[tex]0.02P_1 = 210[/tex]
[tex]P_1 = \frac{210}{0.02}[/tex]
[tex]P_1 = 10500[/tex]
[tex]P_2 = 49500 - P-1 = 49500 - 10500 = 39000[/tex]
Hence:
- $10,500 was invested at 2%.
- $39,000 was invested at 4%.
You can learn more about simple interest at brainly.com/question/25296782
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