Question

You have just sold your house for $1,100,000

in cash. Your mortgage was originally a​ 30-year mortgage with monthly payments and an initial balance of $800,000.

The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 5.25%

​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Monthly payments on the mortgage are $4,542.312011 as follows:

A B C D F 1 Constant Payment Mortgage or Equated Monthly Installments (EMI) Assuming payments at the end of each period 3 EMI is calculated using the formula EMI=[P*r*(1+r)^n]/((1+r)^n]-1 4 Where P= Principal (loan amount), 5 n= Number of installments. ie if N= number of years, n=N*12 6 r= Rate of interest per month in decimals ie. If R= Yearly rate, r=R/(100*12) All amounts in $ 8 Given that 9 Principal (loan amount) (P)= 800000 No. of years (N)= 30 10 Rate of interest (% p.a)=R= 5.5 No. of months (n)= 360 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per month in decimals (r )= R/(100*12) D10/(100*12) 0.004583333 15 No. of months (n)= N*12 G9*12 360 16 (1+r)= 1+G14 1.004583333 17 (1+r)^n= G164610 5.187387841 18 [(1+r)^n]-1= G17-1 4.187387841 19 P*r*(1+r)^n= D9*G14*G17 19020.42208 20 Equated Monthly Insallments (EMI)= [P*r*(1+r)^n]/[(1+r)^n]-1 G19/618 4542.312011

On completion of 18.5 years, number of payments made is 222. At this stage, principal outstanding is $463,781.37 . Relevant portion of the amortization schedule as follows:

Н K M Month oo au wn Shedule of amortization Beginning Monthly Monthly Interest Principal End balance interest payments component Component balance rate =Col (2)*(3) =Col (4)-(5) Col (2)-(6) (2) (3) (4) (5) (6) (7) 800000 0.004583 4542.312011 3666.666667 875.645344 799124.354656 799124.354656 0.004583 4542.312011 3662.653292 879.658719 798244.695937 (1) 1 2 227 228 221 222 223 468581.640816 0.004583 4542.312011 2147.665854 2394.646157 466186.994659 466186.994659 0.004583 4542.312011 2136.690392 2405.621619 463781.373040 463781.373040 0.004583 4542.312011 2125.664626 2416.647384 461364.725656 229

Sale proceeds= $1,100,000

Amount required to pay off the mortgage= $461,781.373040

Therefore, remaining cash after paying off the mortgage= $1,100,000 - $461,781.373040 = $636,218..63