Suppose you buy a new Toyota for $25,000. You obtain a 4-year amortized loan wit

Question

Suppose you buy a new Toyota for $25,000. You obtain a 4-year amortized loan with equal annual payment beginning one year from today (i.e. first payment made one year from today). The quoted interest rate for the loan is 10%, compounded annually

How much will your annual payments be?

Please complete the attached amortization schedule

Year 1

Year 2

Year 3

Year 4

Beginning Balance

$25,000

Interest Paid

Total Payment

Principal Paid

Ending Balance

$0

Assume your car will lose 30% of its market value the first year and further lose $4,000 each year thereafter (i.e. by the end of the first year, your used car can will be sold for $25,000 × (1-30%) = $17,500 on the used car market; and will be sold for $17,500-$4,000=$13,500 on the used car market by the end of year 2; and so on). How much will your used car be worth by the end of year 3 and year 4? Please fill the used car value in the market value schedule.

Year 1

Year 2

Year 3

Year 4

Ending Car Value

$17,500

$13,500

With auto loans, it is common for buyers to trade in their cars after the outstanding principal on the car loan exceeds the re-sale value of the used car. After which loan payment will it be profitable for you to trade-in your car? Why? (hint: the car should be sold if it can be sold for more than the balance owed to the dealer)

Year 1

Year 2

Year 3

Year 4

Beginning Balance

$25,000

Interest Paid

Total Payment

Principal Paid

Ending Balance

$0

Explanation / Answer

Formula for loan amortization = A= [i*P*(1+i)^n]/[(1+i)^n-1] Amt $ A = periodical installment P=Loan amount =             25,000 i= interest rate per period = 10% n=total no of payments                        4 A = [0.10*25000*1.10^4]/[1.10^4-1] =3660.25/0.4641 =7886.77 Schedule Instalment Principal Interest Balance Principal Year 1                7,887                5,387                         2,500                       19,613 Year 2                7,887                5,925                         1,961                       13,688 Year3                7,887                6,518 1369                         7,170 Year 4                7,887                7,170 717                                 0             31,547             25,000                         6,547 Year 1 Year 2 Year 3 Year 4 Beginning Balance $25,000 $19,613 $13,688 $7,170 Interest Paid 2500 1961 1369 717 Total Payment 7887 7887 7887 7887 Principal Paid 5387 5925 6518 7170 Ending Balance $19,613 $13,688 $7,170 $0

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.