If the amortized loan repaid annually with $400, with interest of $45 and rate of 4 percent, the amount of principal in the last month is $530.18
Payment at the end of year 1 = 400
Year increments = 45
Last Payment made = 1480
years left after first payment
[tex]\frac{1480-400}{45} = 24[/tex]
= (1480 - 400) / 45 = 24
Length of the loan = 24 plus 1 = 25 years( the 25th year payment is 1480)
The payment made in the 14th year
400 + (13x45)
= 985
Calculation of Loan balance After 13 Years
25 - 13 = 12
formula for the present value of the loan = P*[1 - (1+r)^-n / r ] + G*[ ((1+r)^n - 1 / r^2*(1+r)^n) - n / r*(1+r)^n ]
P = amount of loan In 14th Year
= 985
r = 4%
n = Number of years = 12
G = 45
We have to put the values in the formula
present value loan balance = 985*[1 - (1+4%)^-12 / 4% ] + 45*[((1+4%)^12 - 1 / 4%^2*(1+4%)^12) - 12 / 4%*(1+4%)^12 ]
Balance after a period of 13 years = 11,370.45
Amount of interest to be paid in the 14th period = Loan balance * Interest rate
= 111370.45 x 0.04
= $454.82
Principal amount = Payment - Interest
Payment = 985
P = 985 - 454.82
Therefore the Principal is = $530.18
The amount of principal after the 14th payment is $530.18
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