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Free_Kalibri [48]
2 years ago
8

Two investments totaling $49,500

Mathematics
1 answer:
zzz [600]2 years ago
5 0

Using simple interest, it is found that:

  • $10,500 was invested at 2%.
  • $39,000 was invested at 4%.

<h3>Simple Interest</h3>

Simple interest is used when there is a single compounding per time period.

The interest after t years in is modeled by:

I(t) = Prt

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 P_1 + P_2 = 49500.
  • One investment yields 2% and the other yields 4%, hence the rates are r_1 = 0.02, r_2 = 0.04.
  • The annual income is of $1770, hence t = 1, I_1 + I_2 = 1770.

Considering the rates, we have that:

I_1 = 0.02P_1

I_2 = 0.04P_2

Considering that I_1 + I_2 = 1770 \rightarrow I_2 = 1770 - I_1:

I_1 = 0.02P_1

1770 - I_1 = 0.04P_2

Adding the equations:

0.02P_1 + 0.04P_2 = 1770

Considering that P_1 + P_2 = 49500 \rightarrow P_2 = 49500 - P_1, we have that:

0.02P_1 + 0.04P_2 = 1770

0.02P_1 + 0.04(49500 - P_1) = 1770

0.02P_1 = 210

P_1 = \frac{210}{0.02}

P_1 = 10500

P_2 = 49500 - P-1 = 49500 - 10500 = 39000

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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Step-by-step explanation:

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i will glad to help in comments
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