Question

3. You have found three investment choices for a​ one-year deposit:10.0 % APR compounded​ monthly, 10.0% APR compounded​ annually, and 9.0% APR compounded daily. Compute the EAR for each investment choice.​ (Assume that there are 365 days in the​ year.) ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

4. Suppose Capital One is advertising a 60​-month, 5.99 %APR motorcycle loan. If you need to borrow$8,000to purchase your dream​ Harley-Davidson, what will be your monthly​ payment?​ (Note: Be careful not to round any intermediate steps less than six decimal​ places.)

5. You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2,356 and you have made every payment on time. The original term of the mortgage was 30​ years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6.375% (APR). How much do you owe on the mortgage​ today? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

1.
EAR=(1+APR/m)^m-1

10% monthly=(1+10%/12)^12-1=10.4713%

10% annually=(1+10%/1)^1-1=10.0000%

9% daily=(1+9%/365)^365-1=9.4162%

2.
Monthly payment=Loan*(rate/12)/(1-1/(1+rate/12)^n)
=8000*(5.99%/12)/(1-1/(1+5.99%/12)^60)

3.
Loan amount=monthly payment/(rate/12)*(1-1/(1+rate/12)^(12*t))
=2356/(6.375%/12)*(1-1/(1+6.375%/12)^(12*30))
=377642.839384

Amount owed today=Loan amount*(1+r/12)^n-monthly payment/(r/12)*((1+r/12)^n-1)
=377642.839384*(1+6.375%/12)^(12*4+8)-2356/(6.375%/12)*((1+6.375%/12)^(12*4+8)-1)
=354899.994657