# Consider a standard mortgage (360 months) with monthly payments and a nominal rate (monthly...

## Question:

Consider a standard mortgage (360 months) with monthly payments and a nominal rate (monthly compounding) of 5.60%. What portion of the payments during the first 33 months goes toward interest?

## Loan Payments:

Loan payments of an amortizable loan are composed of both interest and principal. Payments go largely toward interest at the beginning of a loan's lifespan.

 79.83% of the payment goes towards interest in the first 33 months.

All other factors remaining equal, the original principal value of the mortgage does not matter when calculating the proportional interest expense. We will evaluate the portion of payments that goes towards interest for a loan of both $100,000 and$250,000 to show this. We will use a TVM Solver on a financial calculator to address this question.

$100,000 loan amount: Enter the following into the blank fields of a TVM Solver: N = 360 I% = 5.6 PV = 100000 PMT = ? FV = 0 P/Y = 12 (12 payments per year) C/Y = 12 (12 compounding periods per year) PMT: END (payment is made at the end of each period) Solve for PMT: PMT = -574.079 With the TVM Solver data input in this way, select the SUMINT( function under the financial apps section on the financial calculator. Solve for SUMINT(1,33) which will solve for the amount of interest that was paid in the first 33 months of the mortgage. SUMINT(1,33) = 15122.11432 We now know that$15,122.11 of interest was paid in the first 33 months.

Total payment during the first 33 months = 33 x 574.08

Total payment during the first 33 months = $18,944.64 Portion of payments that went toward interest in first 33 months =$15,122.11/$18,944.64  Portion of payments that went towards interest in first 33 months = 0.79823 or 79.82% We will follow the same process for a$250,000 mortgage to show that the proportion of the payments that goes towards interest does not change if the only input factor that changes is the mortgage amount.

$250,000 loan amount: Enter the following into the blank fields of a TVM Solver: N = 360 I% = 5.6 PV = 250000 PMT = ? FV = 0 P/Y = 12 (12 payments per year) C/Y = 12 (12 compounding periods per year) PMT: END (payment is made at the end of each period) Solve for PMT: PMT = -1435.1974 With the TVM Solver data input in this way, select the SUMINT( function under the financial apps section on the financial calculator. Solve for SUMINT(1,33) which will solve for the amount of interest that was paid in the first 33 months of the mortgage. SUMINT(1,33) = 37805.2858 We now know that$37,805.29 of interest was paid in the first 33 months.

Total payment during the first 33 months = 33 x 1435.20

Total payment during the first 33 months = $47,361.60 Portion of payments that went toward interest in first 33 months =$37,805.29/\$47,361.60

 Portion of payments that went towards interest in first 33 months = 0.79823 or 79.82%