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QuestionLunwabo needs R10 500 in 10 months. He invested R8 000 at 11.5%11.5\% simple interest. How much more does he need?

Studdy Solution

STEP 1

Assumptions1. The required amount for the computer is R10,500. The invested amount is R8,0003. The interest rate is11.5% per annum4. The investment period is10 months5. The interest is calculated as a one-time payment, not monthly compounding

STEP 2

First, we need to find the interest amount on the invested sum. We can do this by multiplying the invested amount by the interest rate and the time in years.
Interest=Invested amounttimesInterest ratetimesTimeInterest = Invested\, amount \\times Interest\, rate \\times Time

STEP 3

Now, plug in the given values for the invested amount, interest rate and time to calculate the interest.
Interest=R8,000times11.5%times1012Interest = R8,000 \\times11.5\% \\times \frac{10}{12}

STEP 4

Convert the percentage to a decimal value and the time to years.
11.%=0.11511.\% =0.11510 months=1012 years10\, months = \frac{10}{12}\, yearsInterest=R8,000times0.115times1012Interest = R8,000 \\times0.115 \\times \frac{10}{12}

STEP 5

Calculate the interest amount.
Interest=R8,000times0.115times1012=R787.50Interest = R8,000 \\times0.115 \\times \frac{10}{12} = R787.50

STEP 6

Now that we have the interest amount, we can find the total amount Lunwabo will have after10 months. This includes both the invested amount and the interest.
Total amount=Invested amount+InterestTotal\, amount = Invested\, amount + Interest

STEP 7

Plug in the values for the invested amount and the interest to calculate the total amount.
Total amount=R,000+R787.50Total\, amount = R,000 + R787.50

STEP 8

Calculate the total amount Lunwabo will have after10 months.
Total amount=R8,000+R787.50=R8,787.50Total\, amount = R8,000 + R787.50 = R8,787.50

STEP 9

Now that we have the total amount Lunwabo will have after months, we can subtract this from the required amount for the computer to find the amount Lunwabo will still be short.
Short amount=Required amount−Total amountShort\, amount = Required\, amount - Total\, amount

STEP 10

Plug in the values for the required amount and the total amount to calculate the short amount.
Short amount=R10,500−R8,787.50Short\, amount = R10,500 - R8,787.50

STEP 11

Calculate the short amount.
Short amount=R10,500−R8,787.50=R,712.50Short\, amount = R10,500 - R8,787.50 = R,712.50The amount that Lunwabo will still be short is R,712.50, which is not an option in the given choices. Therefore, there might be a mistake in the problem or the options provided.

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