Answer:
(a) $668.39
(b) $634.93
(c) $618.20
(d) $584.74
Explanation:
Monthly Payment Formula
![\sf PMT=(Pi\left(1+i\right)^n)/(\left(1+i\right)^n-1)](https://img.qammunity.org/2023/formulas/mathematics/college/b6irf1r1bar0y6jz4hulnhuf5mkwbiwg8w.png)
where:
- PMT = monthly payment.
- P = loan amount.
- i = interest rate per month (in decimal form).
- n = term of the loan (in months).
Given:
- P = $39.950 less any down payment.
- i = 10.25% / 12 = 0.1025/12
- n = 7 years = 7 × 12 = 84 months
Part (a)
Down payment = $0
⇒ P = $39,950
![\implies \sf PMT=(39950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)](https://img.qammunity.org/2023/formulas/mathematics/college/iml6ffvf0gvt18262j1ss8l005gxwk9md8.png)
![\implies \sf PMT = 668.3892086](https://img.qammunity.org/2023/formulas/mathematics/college/2khn6tbwbu6tt7mpbfym3i1k3ca8yqfmn6.png)
Therefore, the monthly payment is $668.39.
Part (b)
Down payment = $2,000
⇒ P = $39,950 - $2,000 = $37,950
![\implies \sf PMT=(37950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)](https://img.qammunity.org/2023/formulas/mathematics/college/t5p821lof0z2a78pdfwxvc3bewc94fe71g.png)
![\implies \sf PMT = 634.9279215](https://img.qammunity.org/2023/formulas/mathematics/college/5fy5rjinipjgoanne4ai60pvyokln78i3d.png)
Therefore, the monthly payment is $634.93.
Part (c)
Down payment = $3,000
⇒ P = $39,950 - $3,000 = $36,950
![\implies \sf PMT=(36950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)](https://img.qammunity.org/2023/formulas/mathematics/college/vipj8v1usiw42hyp54ugs4u8yk13ac527g.png)
![\implies \sf PMT = 618.197278](https://img.qammunity.org/2023/formulas/mathematics/college/ylfehmcsfhfaxkj4cxg7lk00d2o8wgf5ze.png)
Therefore, the monthly payment is $618.20.
Part (d)
Down payment = $5,000
⇒ P = $39,950 - $5,000 = $34,950
![\implies \sf PMT=(34950\left((0.1025)/(12)\right)\left(1+\left((0.1025)/(12)\right)\right)^(84))/(\left(1+\left((0.1025)/(12)\right)\right)^(84)-1)](https://img.qammunity.org/2023/formulas/mathematics/college/8ijsf6x4eqqi7eomjga2ezunkk4sppvkw6.png)
![\implies \sf PMT = 584.735991](https://img.qammunity.org/2023/formulas/mathematics/college/ap4wiu6kqf1xma51ij6musn2c9iaihqyba.png)
Therefore, the monthly payment is $584.74.