Question

Consider the first payment against a $200,000 mortgage that last for 25 years. Fixed repayments are made on a monthly basis. The first row of the amortization schedule is shown below

Payment #12Paymentd…Interest716.67…Debt Paymentp1…Balanceb1…
Calculate p1, the first payment made against the loan principal. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.

Answer 1

1089.08

Explanation:

The interest rate r can be calculated using the information provided as follows

$200,000×r12=$716.67,

which gives r=0.043=4.3% to the nearest 0.1%. We have insufficient information from the table to calculate d, and we must use the formula

P0=d(1−(1+rk)−Nk)(rk),

i.e.

200,000=d(1−(1+0.04312)−25⋅12)(0.04312),

giving

$200,000=183.6407d⟹d=$1,089.08.

Answer 2

Calculating the value of d and the fixed monthly payments against a $200,000 mortgage that last for 25 years

The value of d = $1088.63

fixed monthly payments made = $372

Given that :

Present value ( PV ) $200,000

Period = 25 years

Total period ( n ) = 25 * 12 = 300

also PMT is done monthly

∴ monthly interest rate = ( 716.67 / 200,000 ) * 100 = 0.358% ( r )

i) Next step : Calculate the value of PMT

using the equation below

where : PV = $200,000, r = 0.358% , n = 300

input values into equation

∴ d = PMT = $1088.63

ii) Fixed monthly payments

= d - 716.67

= 1088.63 - 716.67 = $372