Let's say we have a 20 year mortgage with an original loan balance of $150,000 at 5% interest rate per year. How much interest do we pay in the 7th year of the loan? (Paid monthly).

 

interest paid in 7th year of loan is $5834.30

Step-by-step explanation

Loan amount (PV)=150000

Interest rate =5%

Monthly rate =5%/12=0.004166666667

Number of years =20

Number of months in 20 years (n) =20*12 = 240

equal or Monthly Payment formula = PV* i *((1+i)^n)/((1+i)^n-1)

=150000*0.004166666667*((1+0.004166666667)^240)/(((1+0.004166666667)^240)-1)

=989.9336089

Now using Monthly payment, we will calculate balance outstanding as on year 6 and Year 7. Difference between these will be principal payment. Excess of all payments above Principal payment will be interest payment.

So Monthly payment (P)=989.9336089

No of months remaining after 6 years of repayment(n)= (20-6)*12 =168

Unpaid balance formula (PV)=P *(1-(1/(1+i)^n))/i

=989.9336089*(1-(1/(1+0.004166666667)^168))/0.004166666667

=119431.6068

remaining balance of loan amount as on 6th year end =119431.6068

No of months remaining after 7 years of repayment(n)= (20-7)*12 =156

Unpaid balance formula (PV)=P *(1-(1/(1+i)^n))/i

=989.9336089*(1-(1/(1+0.004166666667)^156))/0.004166666667

=113386.7028

remaining balance of loan amount as on 6th year end =113386.7028

Principal repaid = Balance of loan at 6th year - balance of loan at 7th year

=119431.6068-113386.7028

=6044.904

Interest paid during 7th year = (monthly payment*number of months in a year)-principal repaid

=(989.9336089*12)-6044.904

=5834.299307

So interest paid in 7th year of loan is $5834.30