Question

To buy your first home, you take out a 15 year (fully amortizing) mortgage for $400,000 which requires equal yearly payments. The effective annual interest rate is 3.6%. How much principal do you pay off in year 2?
a. $13,659.21
b. $21,318.27
c. $34,977.48
d. $41,895.75
e. None of the above

Answer 1

Answer:

The principal paid off in year two $21,318.27  

Explanation:

The arrangement for equal amount payable yearly to pay off the entire loan obligation (principal plus interest) is an annuity for 15years at 3.6%.

An annuity is a series of equal payment payable annually for certain  number of years where interest is charged at a particular rate.

We can work out the annual equal installment using the Present Value (PV) annuity formula below:

PV = A ×( (1- (1+r)^(-n))/r)

So we can apply this formula to the question

 PV - 400,000, r =3.6%= 0.036, n -15, A is equal instalment, not given.

400,000 = A ×( 1- (1.036)^(-15))/0.036

400,000 = A × 11.4359

A= 400,000/11.4359

A =34,977.47

Equal annual installment =$34,977.47

Now with the help of an amortization table we ascertain the amount of principal paid off in year 2:

Amortization Schedule

Bal @ beginning Interest    Installment Principal Paid Principal bal.

A                      B  = A *3.6% C            D= C - B      E =A-D

400,000.00   14,400.00   34,977.48   20,577.48   379,422.52

379,422.52   13,659.21   34,977.48   21,318.27  

The amortization table is a schedule showing how the loan would be paid over the loan period.

Note that the columns are labelled as A, B, C, D and E starting from the left hand-side respectively

The principal paid off in year two is $21,318.27 which is the bolded figure in  column D,