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QuestionCalculate the time (in years) for R7 520 to grow to R9 841,80 at a simple interest rate of 9,5%9,5 \%. Options: a. 0,33 b. 13,78 c. 2,48 d. 3,25.

Studdy Solution

STEP 1

Assumptions1. The initial investment amount is R7,520. The simple interest rate is9.5% per year3. The final amount after interest is R9,841.804. The interest is calculated as a one-time payment, not monthly compounding

STEP 2

First, we need to find the interest amount. We can do this by subtracting the initial investment from the final amount.
Interest=Final amount−Initial investmentInterest = Final\, amount - Initial\, investment

STEP 3

Now, plug in the given values for the final amount and initial investment to calculate the interest.
Interest=R9,841.80−R7,520Interest = R9,841.80 - R7,520

STEP 4

Calculate the interest amount.
Interest=R9,841.80−R7,520=R2,321.80Interest = R9,841.80 - R7,520 = R2,321.80

STEP 5

Now that we have the interest amount, we can find the time it took for the investment to reach the final amount. We can do this by using the formula for simple interest.
Time=Interest(Initial investmenttimesInterest rate)Time = \frac{Interest}{(Initial\, investment \\times Interest\, rate)}

STEP 6

Convert the percentage to a decimal value.
9.5%=0.0959.5\% =0.095

STEP 7

Plug in the values for the interest, initial investment, and interest rate to calculate the time.
Time=R2,321.80(R7,520times0.095)Time = \frac{R2,321.80}{(R7,520 \\times0.095)}

STEP 8

Calculate the time it took for the investment to reach the final amount.
Time=R2,321.80(R7,520times0.095)=3.25 yearsTime = \frac{R2,321.80}{(R7,520 \\times0.095)} =3.25\, yearsThe investment will reach R,841.80 in3.25 years.

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