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QuestionLindiwe has R80 000 invested at 13.75%13.75\% p.a. and withdraws R25 000 yearly. How many years will this last?

Studdy Solution

STEP 1

Assumptions1. The initial investment amount is R80,000. The interest rate is13.75% per annum, compounded yearly3. Lindiwe withdraws R25,000 at the end of each year for her studies4. The withdrawal starts at the end of the first year

STEP 2

First, we need to find the amount of money left after the first withdrawal. This can be done by first calculating the amount after one year of interest, and then subtracting the withdrawal amount.
Amount after first withdrawal=(Initial amounttimes(1+Interest rate))−Withdrawal amountAmount\, after\, first\, withdrawal = (Initial\, amount \\times (1 + Interest\, rate)) - Withdrawal\, amount

STEP 3

Now, plug in the given values for the initial amount, interest rate, and withdrawal amount to calculate the amount after the first withdrawal.
Amount after first withdrawal=(R80,000times(1+13.75%))−R25,000Amount\, after\, first\, withdrawal = (R80,000 \\times (1 +13.75\%)) - R25,000

STEP 4

Convert the percentage to a decimal value.
13.75%=0.13713.75\% =0.137Amount after first withdrawal=(R80,000times(1+0.137))−R25,000Amount\, after\, first\, withdrawal = (R80,000 \\times (1 +0.137)) - R25,000

STEP 5

Calculate the amount after the first withdrawal.
Amount after first withdrawal=(R80,000times1.1375)−R25,000=R66,000Amount\, after\, first\, withdrawal = (R80,000 \\times1.1375) - R25,000 = R66,000

STEP 6

Now, we will repeat the process for the subsequent years until the amount is less than the withdrawal amount. This will give us the number of full years the investment will finance her studies.

STEP 7

Calculate the amount after the second withdrawal.
Amount after second withdrawal=(R66,000times1.1375)−R25,000=R50,050Amount\, after\, second\, withdrawal = (R66,000 \\times1.1375) - R25,000 = R50,050

STEP 8

Calculate the amount after the third withdrawal.
Amount after third withdrawal=(R50,050times1.1375)−R25,000=R32,056.88Amount\, after\, third\, withdrawal = (R50,050 \\times1.1375) - R25,000 = R32,056.88

STEP 9

Calculate the amount after the fourth withdrawal.
Amount after fourth withdrawal=(R32,056.88times.1375)−R25,000=R11,464.83Amount\, after\, fourth\, withdrawal = (R32,056.88 \\times.1375) - R25,000 = R11,464.83

STEP 10

After the fourth withdrawal, the remaining amount is less than the withdrawal amount. Therefore, the investment will finance her studies for4 full years.
indiwe's investment will finance her studies for4 full years.

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