Question

A young couple buying their first home borrow $85,000 for 30 years at 7.1%, compounded monthly, and make payments of $571.23. After 2 years, they are able to make a one-time payment of $2,000 along with their 24th payment.

(a) Find the unpaid balance immediately after they pay the extra $2,000 and their 24th payment. (Round your answer to the nearest cent.) $

(b) How many regular payments of $571.23 will amortize the unpaid balance from part (a)? Give the answer to one decimal point. payments

(c) How much will the remaining debt be after the number of full payment periods in part (b) is made? (Round your answer to the nearest cent.) $ How much extra must be included with the last full payment to pay off the debt? (Round your answer to the nearest cent.) $

(d) How much will the couple pay over the life of the loan by paying the extra $2,000? (Round your answer to the nearest cent.) $ (e) How much will the couple save over the life of the loan by paying the extra $2,000? (Use your answer from part (b). Round your answer to the nearest cent.) $

Answer 1

we can solve this question by excel.

a.

create amortization table in excel.

missing 24th payment linein snap shot

no of payment payment interest   principle Beg  balance

24 $571.22    $492.99   78.23    $83244.19

25 $571.22 $492.53 78.69 $83165.50

Now balance after 24 th payment and $ 2000 payment = ending balance on 24 th payment - $2000 = $83165.5 - $ 2000 = $ 81165.5

here are excel calculation for table

payment are as per given in question

interest = Beg balance * monthly int rate

principle = payment- interest

next year beg balance of current year ending balance =Beg balance of current year year - principle

b.

here we have to find n that is monthly payment

use nper formula in excel

NO of regular $ 571.23 = =nper( rate, pmt,pv,fv,type)

= nper(0.0059166,-571.23,81165.5,0,0)

= 311.4 monthly payment = 311 payment.

where nper = no of monthly payment

rate = monthly rate = 0.071/12= 0.0059166

pmt = monthly payment

PV= remaining balance of loan value

fv= future value

type = for end mode 0, for beg mode 1

c.

find future value of remaining debt

remaining debt = =fv(rate,nper,pmt,pv,type)

= fv(0.0059166,311,-571.23,81165.5,0)

= -$218.197

extra to be included in monthly payment.

new payment = =pmt(rate, nper,,pv,fv,type)

= pmt(0.0059166,311,81165.5,0,0)

= -$571.48

extra payment = new payment - old payment = $571.48- $571.23 = $0.245

where nper = no of monthly payment

rate = monthly rate = 0.071/12= 0.0059166

pmt = monthly payment

PV= remaining balance of loan value

fv= future value

type = for end mode 0, for beg mode 1

D.

couple total payment

first 24, 571.23 monthly payment = 24*$571.23 = $6854.76

lumpsum payment = $2000

311 monthly payment of 571.23 = 311* $571.23 = $177652.53

remaining debt = $ 218.2

Total payment =  $6854.76 + $2000 + $177652.53 + $ 218.2 = $186725.49

E.

total payment without extra = 360 * $571.23 = $ 205642.8

with extra payment = $ 186725.49

Total saving = $ 205642.8 - $ 186725.49 = $18917.31