Question

You have taken out a 60 -month, $20,000 car loan with an APR of 6%, compounded monehly. The monthly paymont ce the loan is $386.66. Assume that right affer you mako your 50 th payment, the balance of the loan is $3,762:36. How much of your next payment goes toward principal and how much goes foward interest? Compare this with the prinicipal and interest. pald in the fint menth's payment, (Note: Be careful not to round any infermediate steps less than six decimar places.) The amount that goes towards interest is? (Round ta the nearest cent.) Suppose Capital One is advortising a 60 -manth, 5.76% APR moborycle loan. If you need to borrow 58,600 to purchase your dream Harley-Donidson, what wis be your monthy payment? (Nofo: Bip camtut not fo round any intermedide steps less than six desimal places.) Your monthyy payment will be 5 (Round to the noarest cont.) You have been accepted into college, The colege guarantees that your tuiticn will not increase for the four years you attend college. The firat $ to, 900 tuipon payment is doe in aic mentha. Aller that, the same payment is due every six months untt you have made a toul of eight payments. The college cillers a bank account that alows you to withdraw money every six months and has a fixed APR of 3.9% (with semiannual compounding) guaranteed to remain the same over the neet four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the iast payment is made? (Noter Be careful not to round any intermediace sieps fess than ef decinal phices) The amount of money you must deposit teday is $ (Round to the nearest cent.)

Answer 1

The 51st car loan payment's interest is $18.81 with the principal being $367.85. The monthly motorcycle loan payment is approximately $176.05. To make eight $10,900 tuition payments on schedule, an initial deposit of approximately $16,036.75 is required.

Step-by-step explanation:

To calculate the portions of the 51st payment going toward interest and principal for a car loan following the provided scenario: First, we will calculate the interest portion using the formula Interest = Remaining balance × Monthly interest rate. With an APR of 6%, the monthly interest rate is 0.06/12 = 0.005. Therefore, the interest for the 51st payment is $3,762.36 × 0.005 = $18.81. The remaining part of the payment, $386.66 - $18.81 = $367.85, goes toward the principal.

To calculate the monthly payment for a 60-month motorcycle loan at a 5.76% APR, we use the loan payment formula. The calculation yields a monthly payment of approximately $176.05.

Lastly, to find the initial deposit needed for a series of tuition payments, we use the future value of an annuity formula. The calculation shows the required initial deposit would be approximately $16,036.75.