Question

1. You plan to borrow $75,000 to purchase a small yacht, 2014 Maritimo X50, with financing from Capital One Bank. You can afford to make monthly payments of $1,475, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan? What is the APR on this loan? What is the EAR on this loan? Prepare an amortization schedule on the 60-month yacht loan and determine the total interest paid after 5 months. (Help Please)

Answer 1

given,

Principal Loan      PV        =      $ 75000

Period        n       =          60month  

monthly payment   PMT =     $ 1475

now we need to find the rate at which a 75000 loan for 60 months will match a 1475 monthlly payment

rate is determined with the rate function,

but the above rate is monthly rate, so the APR = 0.559522 X12   = 6.71%

the highest rate that can be afforded is 6.71%

or APR    is 6.71%

the excel formula is

te

EAR of the loan      

                                              =   (1 +    0.0671 /12 )¹²     -   1

                                             = ( 1+    0.00591667)¹²     - 1

                                            =     1.06920 -1

                                            = 0.0692

                     EAR                = 6.92%

60 month amortisation schedule

opening loan balance is 75000

equated monthly payment for all 60 months is 1475. this amount is split into interest and principal

interest is computed on the opening loan balance at 6.71% interest   and divided by 12 - since monthly

from 1475 the above interest amount is reduced to arrive at the principal

this principal portion is reduced from the opening loan amount to arrive at the closing loan amount.

this closing loan amount will be the opening loan amount for the next month

amortization schedule is

excel   formulas

the total interest paid after 5 months is $ 2038.75   the same is highlighted in yellow color in the amortisation table