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5. Tia invests $2,500 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 5 years? Look at the concept summary if you forgot the formula for compound interest.​

Respuesta :

Answer:

$3050.48

Step-by-step explanation:

If 4% is compounded quarterly, that means it's 1% every quarter. since we have 5 years, that's 1.01^20, which is approx. 1.2202. We multiply this by the orignal $2500, so our investment at the end of 5 years is $3050.48 (rounded to nearest cent)

Lanuel

The amount of money that Tia's investment would be worth at the end of 5 years is equal to $3050.5.

Given the following data:

  • Principal = $2,500
  • Interest rate = 4% = 0.04
  • Time = 5 years
  • Number of times = 4

To determine how much is the investment worth at the end of 5 years:

Mathematically, compound interest is given by the formula:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where;

  • A is the future value.
  • P is the principal (starting amount).
  • r is annual interest rate.
  • n is the number of times the interest is compounded in a year.
  • t is the number of years for the compound interest.

Substituting the given parameters into the formula, we have;

[tex]A = 2500(1 + \frac{0.04}{4})^{4\times 5}\\\\A = 2500(1 +0.01)^{20}\\\\A = 2500(1.01)^{20}\\\\A = 2500(1.2202)[/tex]

Future value, A = $3050.5

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