Vanessa decides to invest R 140,000 into an account earning 13.5% interest per year, compounded quarterly. This new account allows her to withdraw an amount of money every quarter for ten years after which time the account will be exhausted. The amount of money that Vanessa can withdraw every quarter is
[1] R 3500.00
[2] R 1704.28
[3] R 6429.28
[4] R 8594.82
[5] none of the above
You can rule out answer #1 immediately: there are 40 withdrawals, and 40 x 3500 is 140,000, the original deposit. This would be the answer if there was no interest, but there is interest, so this answer is wrong.
Now you can also rule out answer #2, because it is less than answer #1, and earning interest will enable Vanessa to withdraw more than not earning interest.
You can do a complicated calculation at this point, but because #3 and #4 are so far apart, here's what I would do. 13.5 / 4 is 3.375%. 3.375% of 140,000 is 4,725 - that's the interest earned in the very first quarter. In the last quarter, there will be almost no interest earned (or none, if the interest is on the amount after withdrawal.) So I halve that number for an average. This is just a rough calculation. I get 2362.5. Now the actual amount of the interest will be more than that at the beginning, so she will withdraw less principal, and less than that at the end, so she will withdraw more principal. It isn't linear, so assuming that the interest or the principal can be averaged is not correct, but it's an approximation that is useful because it is easy.
The total of 3500 and 2362.5 is 5862.5. This is much closer to answer #3 than to answer #4. Depending on how much time I had for the test or homework, I might just answer #3 at this point. But if I had time, I would test that answer. After 1 quarter she has earned 4,725 interest and withdrawn 6429.28, so her balance is [you tell me] and then in the next quarter she would earn [you tell me] and so on. If you don't want to do that 40 times in a spreadsheet or whatever and you've been taught the overall formula for what the balance is after n periods, use that. If it works out that she withdraws all the money, you now know for sure that #3 is correct.
One caution - the "none of the above" answer means that if the real answer is say 6429.75, the correct answer is #5 not #3. This makes it more important to accurately test the answer that seems to be approximately correct. Who knows how close your instructor expects your calculation to be?
Applying the standard loan equation derived here:
r = 13.5/100/4
s = 140000
n = 4*10
d = r (1 + 1/(-1 + (1 + r)^n)) s = 6429.28
where
r = periodic interest rate
s = principal
n = number of periods
d = periodic payment
