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Radhika is refinancing a business loan and is considering 2 different loan offers. Under Offer 1, the loan's initial principal would be $190,000, and she would pay down $1,250 in principal with each monthly payment during the first year of the loan. Under Offer 2, $4,000 in refinancing fees would be added to bring the principal to $194,000, but she would pay down $1,775 in principal with each monthly payment during the first year of the loan.
In the first column of the table, select the amount of principal that would remain after 12 monthly payments under Offer 1. In the second column of the table, select the amount of principal that would remain after 12 monthly payments under Offer 2. Make only two selections, one in each column.
$168,700
$171,000
$172,700
$175,000
$176,700
$179,000
We'll use a timeline to track the principal reduction over 12 months:
Offer 1 Timeline:
Start ----[Month 1]----[Month 2]----...----[Month 12]---- End $190,000 -$1,250 -$1,250 -$1,250 = ?
Offer 2 Timeline:
Start ----[Month 1]----[Month 2]----...----[Month 12]---- End $194,000 -$1,775 -$1,775 -$1,775 = ?
| Offer | Initial Principal | Monthly Principal Payment | Time Period |
| 1 | $190,000 | $1,250 | 12 months |
| 2 | $194,000 | $1,775 | 12 months |
We need to find:
The calculation for each offer follows:
\(\mathrm{Remaining\ Principal} = \mathrm{Initial\ Principal} - (\mathrm{Monthly\ Payment} \times \mathrm{Number\ of\ Months})\)
Initial principal: $190,000
Monthly principal reduction: $1,250
Total reduction over 12 months: \(\$1,250 \times 12 = \$15,000\)
Remaining principal = \(\$190,000 - \$15,000 = \$175,000\)
Initial principal: $194,000
Monthly principal reduction: $1,775
Total reduction over 12 months: \(\$1,775 \times 12 = \$21,300\)
Remaining principal = \(\$194,000 - \$21,300 = \$172,700\)
Our calculations show:
Both values appear in our answer choices, confirming our calculations are correct.
Final Answer: