Question

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).

rhonda wants to take out a 30-year, $280,000 loan with a 4.4% apr. she is considering purchasing 2 points, which will decrease her apr by 0.125% per point. each point will cost 1% of her loan. compare her monthly payments without and with the purchase of the points.
without points
with points

Explanation:

Step1: Calculate monthly rate (no points)

Monthly rate: $\frac{0.044}{12} \approx 0.003667$

Step2: Calculate total payments (no points)

Total payments: $30 \times 12 = 360$

Step3: Compute monthly payment (no points)

Use loan formula: $M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$

$$ M = 280000 \times \frac{0.003667(1+0.003667)^{360}}{(1+0.003667)^{360} - 1} \approx 1,401.37 $$

Step4: New APR with points

New APR: $4.4\% - (2 \times 0.125\%) = 4.15\%$

Step5: New monthly rate (with points)

Monthly rate: $\frac{0.0415}{12} \approx 0.003458$

Step6: Compute monthly payment (with points)

$$ M = 280000 \times \frac{0.003458(1+0.003458)^{360}}{(1+0.003458)^{360} - 1} \approx 1,353.64 $$

Answer:

Without points: $\$1,401.37$
With points: $\$1,353.64$