Respuesta :

elijahpierre672

Answer:

The answer is T = 300 years.

Step-by-step explanation:

The formula for simple interest is I = PRT, where I is the interest, P is the principal amount (initial investment), R is the annual interest rate (in decimal form), and T is the time in years.

In this case, the interest I is the final amount minus the initial investment, which is $5,505.50 - $4,550 = $955.50. The principal P is $4,550, and the annual interest rate R is 7% or 0.07 in decimal form. We want to find the time T.

Substituting these values into the formula gives us:

955.50 = 4550 × 0.07 × T

Solving for T gives us:

T = 955.50 / 4550 × 0.07

Calculating the above expression gives us the time in years.

T = 3.00 years.

msm555

Answer:

3 years

Step-by-step explanation:

The formula for calculating simple interest is given by:

[tex]\sf I = P \cdot r \cdot t [/tex]

where:

  • [tex]\sf I [/tex] is the interest earned,
  • [tex]\sf P [/tex] is the principal amount (initial investment),
  • [tex]\sf r [/tex] is the annual interest rate (as a decimal),
  • [tex]\sf t [/tex] is the time the money is invested or borrowed for.

In this case:

  • [tex]\sf P = \$4,550 [/tex],
  • [tex]\sf r = 0.07 [/tex] (7% expressed as a decimal),
  • [tex]\sf I = \$5,505.50 - \$4,550 = \$955.50 [/tex].

Now, rearrange the formula to solve for [tex]\sf t [/tex]:

[tex]\sf t = \dfrac{I}{P \cdot r} [/tex]

Substitute the known values:

[tex]\sf t = \dfrac{955.50}{4550 \cdot 0.07} [/tex]

Now, calculate [tex]\sf t [/tex]:

[tex]\sf t \approx \dfrac{955.50}{318.50} [/tex]

[tex]\sf t \approx 3 \, \text{years} [/tex]

Therefore, it will take approximately 3 years for the investment to reach $5,505.50 with a simple interest rate of 7% per annum.

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