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%.
