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You have $5,000 to invest and want it to grow to $20,000 in two years. What interest rate would you need to find to make this possible?I wan answer and explanation.

Sagot :

ANSWER

The interest rate is 150%

EXPLANATION:

Given that;

The initial amount is $5000

The total amount $20, 000 after 2 years

Total period of the investment is 2 years

To find the interest rate, follow the steps below

1. Find the interest on the investment after two years

In the given data,

The initial amount (principal) is $5000

The total amount after 2 years is $20, 000

Recall that,

Total amount = Interest + principal

20, 000 = interest + 5000

subtract 5000 from both sides of the equation

20, 000 - 5,000 = interest + 5000 - 5000

15,000 = interest

Therefore, the interest on the investment after 2 years is $15, 000

Step 2; Find the interest rate using the simple interest formula

[tex]\text{ I }=\text{ }\frac{P\times R\times T}{100}[/tex]

Where

I is the interest

P is the principal

R is the interest rate

T is the time of the investment

[tex]\begin{gathered} \text{ 15, 000 }=\text{ }\frac{5000\times\text{ r}\times\text{ 2}}{100} \\ \text{ } \\ \text{ 15000 }=\text{ }\frac{10,000r}{100} \\ \text{ 15, 000 }=\text{ 100r} \\ \text{ Divide both sides by 100} \\ \frac{15,000}{100}\text{ }=\text{ }\frac{100r}{100} \\ \text{ r }=\text{ 150\%} \end{gathered}[/tex]

Therefore, the interest rate is 150%