Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
