Question

You have just taken out an amortized loan for $404,000. Assume that the loan will be paid in 24 equal monthly installments of

​$18,345.62​ and that the first payment will be due 1 month from today. How much of your third monthly payment will go toward the repayment of​ principal? Fill in the worksheet below.  

Month	Interest Owing at End of Month​ ($)	Principal Repayment​ ($)	Principal Owing at End of Month​ ($)
1
2
3

Answer 1

Solution

Here we have principal = 404000

Time= 24 months

EMI= 18345.62

Using the PV of annuity formula we can calculate the rate of interest

PV of annuity= Annuity*[1-(1/(1+r)^n)]/(r/12)

PV of the annuity is the principal amount

r= rate of interest

Putting the values

404000= 18345.62*[1-(1/(1+r)^24)]/(r/12)

Solving we get

r=.084

=8.4%

Now using this r we get the below sheet

Excel formula

The excel format as asked is given below

Month	Monthly Interest owning at the end of month	Principal repayment	Principal owning at the end of month
1	2828	15517.62	388482.38
2	2719.37666	15626.24334	372856.1367
3	2609.992957	15735.62704	357120.5096

Thus Principal payment in the third month is 15735.62704

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