Question

John House has taken a $250,000 mortgage on his house at an interest rate of 6 percent per year. If the mortgage calls for 20 equal, annual payments, what is the amount of each payment?

Answer 1

To find the amount of each annual payment for a $250,000 mortgage at a 6% interest rate with 20 equal annual payments, the annuity payment formula is used, substituting the principal, rate, and number of payments into the formula and solving for the payment amount.

Step-by-step explanation:

The student is asking for the amount of each annual payment for a $250,000 mortgage at an interest rate of 6% with 20 equal annual payments. To solve this problem, one should apply the annuity formula for equal payments, and the formula for an amortizing loan could be used.

The annuity payment (A) can be calculated using the formula: A = P * [ i / (1 - (1 + i)^-n)], where:

P is the principal amount ($250,000),

i is the annual interest rate divided by the number of compounding periods per year (0.06 in this case as payments are annual), and

n is the total number of payments (20).

The question requires finding the equal annual payment which involves algebraic manipulation after substituting the known values into the formula. A financial calculator or software package that includes financial functions can simplify this computation. In absence of such tools, one could manually calculate the payment.

Answer 2

$21,796.14

Step-by-step explanation:

Use the Time Value of Money techniques to calculate the amount of each installment (PMT)

PV = $250,000

i = 6 %

n = 20

P/yr = 1

FV = $0

PMT = ?

Using a Financial calculator to input the values as above, each annual instalment/payment will be $21,796.14.