# Borrowing money To pay for college, a student borrows $5000 interest-free from his father. If he pays his father back at the rate of$200 per month, how much will he still owe after 12 months?

Borrowing money To pay for college, a student borrows $5000 interest-free from his father. If he pays his father back at the rate of$200 per month, how much will he still owe after 12 months?
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Formula used:
The arithmetic sequence is a sequence of the form $a,a+d,a+2d,\dots ,a+\left(n—1\right)d,\dots$ Where a is the first term, nth term $=a+\left(n—1\right)$ dand dis the common difference.
Calculation:
Here, the borrow amount is 5000.
Compute the first month balance to subtract borrow amount 5000 and pay back amount 200.
First month balance $=5000—200=4800$
Compute the second month balance to subtract borrow amount 4800 and pay back amount 200.
Second month balance $=4800—200=4600$
Compute the third month balance to subtract borrow amount 4600 and pay back amount 200.
Third month balance $=4600—200=4400$
The monthly balance borrow amount form an arithmetic sequence 4800, 4600, 4400...
Compute the common difference by subtracting the any two consecutive terms.
$d=4600—4800=-200$
The common difference is $d=—200$.
Obtain the balance owe amount after 12 month by substituting $a=4800,d=—200$ and $n=12$ in the nth term formula.
${a}_{12}=4800+\left(12—1\right)\left(-200\right)$
$=4800+11\left(—200\right)$
$=4800-2200$
$=4800-2200=2600$
Hence, after 12 month he owes \$2600.
Jeffrey Jordon