Problem

Solve each applied problem by writing the first f…

Problem 27 Easy Difficulty

Solve each applied problem by writing the first few terms of a sequence.
Horacio Loschak borrows $\$ 1000$ and agrees to pay $\$ 100$ plus interest of $1 \%$ on the unpaid balance each month. Find the payments for the first six months and the remaining debt at the end of that period.

Answer

$$
\$ 110, \$ 109, \$ 108, \$ 107
$$ $$
\$ 106, \$ 105 ; \$ 400
$$

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Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 1

Sequences and Series

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Video Transcript

Okay, So this problem you have, um, someone that bar $2000 he's paying it back by paying $100 plus 1% of the unpaid amount are each time you want to get the 1st 6 months. You want to realize how much more to the O after six months? So, um, so First versatile, he's gonna pay $100 plus 1% of $1000 because he hasn't paid that any of the $1000 yet. So that's gonna equal 100. Plus 1% of 1000 is 10. So he's gonna pay 100 and $10 that first time. And so what's left? This will be what's left this column right here. And that's gonna be 8 90 because it would take 100 and 10 minus 2000 and 8 90 So the next bond, he's gotta pay $100 plus 1% of the 8 90 okay? And that's gonna equal 108 $100.+108 0.9 90 cents. So he's gonna be left with. He's getting That's gonna equal. I'm sorry. So it's gonna equal. Just do this. So you can get, that's gonna be 8 90 So he's gonna pay 10 $808.90. When he does that, he's gonna have $781.10 left to pay. Next month, he's gonna pay $100 plus 1% of the 70 81 10 and that's gonna equal $100 plus $7.81 around to the nearest 100 place each time. Now, the 107 um, one of $7.81. That's gonna leave him with $673.29 next month. He's not $100. He's gonna pay 1% of the 6 73 of sorry Of the 6 73 29 that would be $100 plus, um, 1% of 6 73 is gonna be 6.73 and that's gonna equal $106.73. And then that's gonna mean what he has left is $566.56 and you keep going two more times 1% of the 56 Ah, If the 556 56. That's equal $100 plus $5.67 as equal $105.67. When you subtract that from the 5 66 amount you're going to get 4 60 ah, 89 then one more time, $100 plus 1% of the for 60 89 an ethical 100 plus $4.61. If I'm rounding, that's $104.61. When he pays that, he's gonna have $356.28 left to pay.

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