Radhika is refinancing a business loan and is considering 2 different loan offers. Under Offer 1, the loan's initial principal...
GMAT Two Part Analysis : (TPA) Questions
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.
Phase 1: Owning the Dataset
Visual Representation
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 = ?
Key Information Summary
| Offer | Initial Principal | Monthly Principal Payment | Time Period |
| 1 | $190,000 | $1,250 | 12 months |
| 2 | $194,000 | $1,775 | 12 months |
Phase 2: Understanding the Question
We need to find:
- Column 1: Principal remaining after 12 months under Offer 1
- Column 2: Principal remaining after 12 months under Offer 2
The calculation for each offer follows:
\(\mathrm{Remaining\ Principal} = \mathrm{Initial\ Principal} - (\mathrm{Monthly\ Payment} \times \mathrm{Number\ of\ Months})\)
Phase 3: Finding the Answer
Calculating Offer 1
Initial principal: $190,000
Monthly principal reduction: $1,250
Total reduction over 12 months: \(\$1,250 \times 12 = \$15,000\)
Remaining principal = \(\$190,000 - \$15,000 = \$175,000\)
Calculating Offer 2
Initial principal: $194,000
Monthly principal reduction: $1,775
Total reduction over 12 months: \(\$1,775 \times 12 = \$21,300\)
Remaining principal = \(\$194,000 - \$21,300 = \$172,700\)
Phase 4: Solution
Our calculations show:
- Offer 1: $175,000 remaining after 12 months
- Offer 2: $172,700 remaining after 12 months
Both values appear in our answer choices, confirming our calculations are correct.
Final Answer:
- Column 1 (Offer 1): $175,000
- Column 2 (Offer 2): $172,700