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How long does it take $500 to double at a simple interest rate of 24%?

Sagot :

semsee45

Answer:

4 years and 2 months

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • t = time (in years)

Given:

  • A = $500 × 2 = $1,000
  • P = $500
  • r = 24% = 0.24

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 1000 = 500(1 + 0.24t)[/tex]

[tex]\implies \sf \dfrac{1000}{500}=(1 + 0.24t)[/tex]

[tex]\implies \sf 2=1 + 0.24t[/tex]

[tex]\implies \sf 1 = 0.24t[/tex]

[tex]\implies \sf t=\dfrac{1}{0.24}[/tex]

[tex]\implies \sf t=4 \frac{1}{6} \:years[/tex]

[tex]\implies \sf t=4\:years\:2\:months[/tex]

Therefore, it takes 4 years and 2 months for the initial investment of $500 to double at a simple interested rate of 24%.

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