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Yield to Maturity and the Yearly Payment on a Fixed-Payment Loan

You decide to purchase a new home and need a $100,000 mortgage. You take out a loan from the bank that has an interest rate of 7%. What is the yearly payment to the bank to pay off the loan in twenty years?

Solution

The yearly payment to the bank is $9,439.29.

LV=FP/1+i + FP/(1+i)² + FP/(1+i )³ + …… + FP/(1+i)^n

where

LV=loan value amount=$100,000

i =annual interest rate =0.07

n =number of years =20

Thus

$100,1000=FP/1+0.07 + FP/(1+0.07)² + FP/(1+0.07 )³ + ……. + FP/(1+0.07)^20

To find the monthly payment for the loan using a financial calculator:

n=number of years =20

PV=amount of the loan(LV) =-100,000

FV= amount of the loan after 20 years =0

i= annual interset rate =0.07

Then push the PMT button = fixed yearly payment (FP)=$9,439.29