If You Invest $3,900 At A 7.83% Simple Annual Interest Rate, Approximately How Long Will It Take For You To Have $10,000?A. 12 Years B. 15 Years C. 20 Years D. 30 Years Please Select The Best Answer From The Choices Provided.

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What is Simple Interest?

Simple interest is a type of interest that is calculated only on the initial principal amount. It does not take into account the interest that has already been earned. The formula for calculating simple interest is:

Simple Interest Formula

A = P(1 + rt)

Where:

  • A = the total amount after time t
  • P = the principal amount (initial investment)
  • r = the annual interest rate (in decimal form)
  • t = the time the money is invested for (in years)

What is Compound Interest?

Compound interest is a type of interest that is calculated on both the initial principal amount and any accrued interest. It takes into account the interest that has already been earned. The formula for calculating compound interest is:

Compound Interest Formula

A = P(1 + r/n)^(nt)

Where:

  • A = the total amount after time t
  • P = the principal amount (initial investment)
  • r = the annual interest rate (in decimal form)
  • n = the number of times interest is compounded per year
  • t = the time the money is invested for (in years)

Calculating Time for Simple Interest

In this problem, we are given the principal amount (P) as $3,900, the annual interest rate (r) as 7.83%, and the target amount (A) as $10,000. We need to calculate the time (t) it will take for the investment to reach $10,000.

Given Values

  • P = $3,900
  • r = 7.83% = 0.0783 (in decimal form)
  • A = $10,000

Time Calculation

We can rearrange the simple interest formula to solve for time (t):

t = (A - P) / (r * P)

Substituting the given values, we get:

t = ($10,000 - $3,900) / ($3,900 * 0.0783) t ≈ 12.35 years

Rounding to the Nearest Whole Number

Since we are given multiple-choice options, we can round the calculated time to the nearest whole number. In this case, the calculated time is approximately 12.35 years, which rounds to 12 years.

Conclusion

Based on the calculation, it will take approximately 12 years for the investment of $3,900 at a 7.83% simple annual interest rate to reach $10,000.

Answer

The correct answer is A. 12 years.