SOLUTION: A person borrows $2000 at 10%. He agrees to pay off the debt with payments of size $X, $2X, and $4X
in 3 months, 6 months and 9 months respectively. Determine X using focal date
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in 3 months, 6 months and 9 months respectively. Determine X using focal date
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Question 1177866: A person borrows $2000 at 10%. He agrees to pay off the debt with payments of size $X, $2X, and $4X
in 3 months, 6 months and 9 months respectively. Determine X using focal date
a. at the present;
b. in 3 months. Found 2 solutions by Solver92311, greenestamps:Answer by Solver92311(821) (Show Source):
(1) With nothing stated otherwise, we can assume the interest is simple interest applied to the balance at the end of each 3 months, just before each payment is made.
(2) I don't know what "focal date" is. The following is a straightforward method of solving the problem.
10% (annual) interest means 2.5% interest for each quarter (3 months), so during each 3-month period the balance grows by a factor of 1.025.
Initial balance: $2000.00
Balance at the end of 3 months: $2000.00(1.025) = $2050.00
Balance after first payment: $2050.00-X
Balance at the end of 6 months: ($2050.00-X)(1.025) = $2102.25-1.025X
Balance after second payment: $2102.25-1.025X-2X = $2102.25-3.025X
Balance at the end of 9 months: ($2102.25-3.025X)1.025
Balance after third payment: ($2102.25-3.025X)1.025 - 4X
The balance is to be zero after the third payment:
Solution using a graphing calculator shows X = $303.47.
