A sum of $6600 was taken as loan. This is to be repaid in two annual
[#permalink]
25 Oct 2020, 21:07
(1st) Chart the sequence of Events
We will receive $6,600 the 1st year
throughout the year 20% Interest will accrue such that at this point, by the END of the 1st Year, we will have to pay back:
$6,600 * (1.2) = $6,600 * (6/5) -----> in Total
However, we are breaking up the Payments we pay back Each Year in 2 Equal Installments. Let the amount we pay back at the End of Year 1 = $X
Beg of Year 1: $6,600
Throughout Year 1: $6,600 * (6/5) is the amount we have to pay back so far
END of Year 1 we pay Back $X Installment so the amount Remaining:
$6,600 * (6/5) - $X
Beginning of Year 2 the Amount we still owe from the Loan is:
$6,600 * (6/5) - $X
Throughout Year 2 we will have to pay back 20% Interest on top of the Remaining Money we still owe:
[ $6,600 * (6/5) - $X ] * (6/5)
END of Year 2:
we want the Installment we pay back to EQUAL the Same Amount we paid back at the end of Year 1 (the Question says 2 Installments)
Therefore, the Amount we pay back at the End of Year 2 should be:
[ $6,600 * (6/5) - $X ] * (6/5) = $X
and now we have paid back the loan in 2 Equal Installments = $X
Q: What is the amount of the Installment?
or
What is $X = ?
Use the Equation Set up at the End of Year 2 to Solve for $X
[ (6,600) * (6/5) - X ] * (6/5) = X
----Distribute (6/5) through the Brackets-----
(6,600) * (6/5) * (6/5) - X * (6/5) = X
----Add: X * (6/5) to Each Side of the Equation----
(6,600) * (6/5) * (6/5) = (11/5) * X
----Cancel a 5 in the Denominator on Each Side of the Equation (i.e., Multiply Both Sides by *5)-----
(6,600) * (6/5) * (6) = (11) * X
---Cancel a Factor of 11 in the Numerator on Each Side of the Equation (i.e., Divide Both Sides by /11) -----
(600) * (6/5) * (6) = X
Solving For X ----->
(120) * (6) * (6) = (720) * (6) = 4,320
The Installment Payments Each Year on the Loan = $4,320
-A-
Tricky Question unless you know the Formula for Installment Payments on a Loan....