Question 1111422: Can someone please explain this question to me in depth
How much, to the nearest rand, can Lerato borrow from a bank if she can repay the loan by means of
quarterly payments of R2 000, starting at the end of the first quarter? The interest rate is 18% per annum,
compounded quarterly and the duration of the loan is 10 years.
[1] R214 061
[2] R15 825
[3] R36 803
[4] R17 504
l do not understand this part, starting at the end of the first quarter?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The answer is  .
What the wording means is that the first R2 000 payment is due
exactly 1 quarter (3 months) after receiving the loan.
At that time, the bank
adds to the amount owed  times the amount owed,
and subtracts the R2 000 received at that time.
The new balance would be
 .
A quarter later, the bank adds a quarter worth of interest on R36459.14,
and Lerato pays another R2 000.
The balance then is
 .
At  after taking the loan,
Lerato would make the last R2 000 payment,
and the balance owed would be zero.
You may have been taught that to calculate that R36 803 you had
to use a factor from a table, or
to use software, or
to use a formula.
I used the function PV (present value) in a Microsoft Excel spreadsheet,
entering  as Rate (per quarter),
 for Nper (the number of periods, or equal payments),
 for PMT (the amount of each payment),
 for FV (future value),
and 0 (no entry) for "Type" (meaning payments made at the end of each period).
I got the same number calculating
 .
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