about this questionwhat is the formula that we should use in this question And h

Question

about this questionwhat is the formula that we should use in this question And how to calculate those in the finance calculator u a house for 00,co ond fnance it using a 3 year mortgage The anncal&&Find; the mon tily Payment. and the int and Dnea paid in month 14 o 157,3 ad in the 3th year year an yeac 19 +"month-wo 5.5060 157 month- 1,093.72 Principal 2,453.240 21H33. 100 4.027 293.09 e 3, 381 3019 S, (o4 132 01 306 9488 390,' 3%""month 659.CSG 3 ear 9293 alth year 20,324.8433 27th year -91OG th

Explanation / Answer

We can use following Present Value of an Annuity formula to calculate the monthly loan payment with 6% interest rate on the loan

PV of loan = PMT * [1-(1+i) ^-n)]/i

Where

Present value of loan (PV) = $500,000

Monthly loan payment PMT =?

Number of payments n = 30 years * 12 = 360 months

Annual interest rate I =6%, therefore monthly interest rate i=6%/12 = 0.5% or 0.005

Therefore

$500,000 = PMT * [1- (1+0.005) ^-360]/0.005

Or PMT = $2,997.7526

Now to calculate Principal paid in 19th month, first we have to calculate the PV of loan at the end of 19th month and then PV of loan at the end of 18th month.

Principal paid in 19th month = PV of loan at the end of 18th month - PV of loan at the end of 19th month

To calculate the present value of loan, we can use same formula as above only the value of remaining number of payments n will change.

For 18th month; n = 360 -18 = 342; PV = $490,649.3247

And for 19th month; n = 360 -19 = 341 = $490,104.8187

Therefore Principal paid in 19th month =$490,649.3247 - $490,104.8187 = $544.5060

Principal paid in 26th month = PV of loan at the end of 25th month - PV of loan at the end of 26th month

= $486,780.1308 - $486,216.2788 = $563.85197

Principal paid in 157th month = PV of loan at the end of 156th month - PV of loan at the end of 157th month

= $382,805.4744 - $381,721.7492= $1,083.7252

Principal paid in 340th month = PV of loan at the end of 339th month - PV of loan at the end of 340th month

= $59,619.2420 - $56,919.5856 = $2,699.65642

Principal paid in 13th year = PV of loan at the end of 12th year - PV of loan at the end of 13th year

For 12th year; n = 360 -12*12 = 360 -144 = 216

For 13th year; n = 360 -12*13 = 360 -156 = 204

Principal paid in 13th year = $395,397.20 - $382,805.47 = $12,591.7301

Principal paid in 21th year = PV of loan at the end of 20th year - PV of loan at the end of 21th year

For 20th year; n = 360 -12*20 = 360 -240 = 120

For 21st year; n = 360 -12*21 = 360 -252 = 108

Principal paid in 21st year = $270,017.93 - $249,693.08 = $20,324.8493

Principal paid in 27th year = PV of loan at the end of 26th year - PV of loan at the end of 27th year

For 26th year; n = 360 -12*26 = 360 -312 = 48

For 27th year; n = 360 -12*27 = 360 -324 = 36

Principal paid in 27th year = $127,645.26 - $98,539.18 = $29,106.0842

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