help please Challenge Problem 2 points Suppose that you inve

Challenge Problem: [2 points] Suppose that you invest a total of $10,000 in two investments. The first investment pays 5% interest compounded monthly. The second investment pays 7.2% interest corn pounded daily. How much was invested in each account if after two years the total value of the two investments is $11,507.02. (Round your answers to the nearest cent.)

Solution

Given that a total of $10,000 in two investements

The amount invested in each account is

first account $794 and interest is $83.33 and after 2years total investement is $877.33

second account $9206 and interest is $1423.69 and after 2 years total investement is $10629.69

so after two years the total value of the two components is $11,507.02

First let us assume that you invested 794$ in the first investement as it pays 5% interest compounded monthly

To find we use formula A=P(1+r/n)^n.t                                       

A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years

We have,

P=$794 , r=5% , n=12 and t=2 years

after applyinh all those values into the above formula,

A=794(1+0.05/12)^12.2

A=794(1.004167)²⁴

A=794(1.10495)

A=877.33

To find the intereset we use the formula A=P+I, since A=877.33 and P = 794 we have

A=P+I

877.33=794+I

I=877.33794

I=83.33

hence first investement pays 83.33$  for 2 years . so, the total amount for 2 years is$877.33

  First let us assume that you invested $9206 in the first investement as it pays 7.2% interest compounded daily

We use the same above formula

P=$9206 , r=7.2% , n=365 and t=2 years

AAAA=9206(1+0.072/365)^365.2

A=9206(1.000197)⁷³⁰

A=92061.154648

A=10629.69

To find interest we use formula A=P+I, since A=10629.69 and P = 9206 we have:

10629.69=9026+I

I=10629.699206

I=1423.69