Question

A partially amortizing mortgage is made for $60,000 for a term of 10 years. The borrower and lender agree that a balance of $20,000 will remain and be repaid as a lump sum at that time. a. If the interest rate is 7 percent, what must monthly payments be over the 10-year period

Answer 1

Answer:

The monthly payments will be $464.44

Explanation:

in this problem we are given the present value of the annuity or house which is $60000 - $20000 = $40000 we subtract because the $20000 will be paid as a lumpsum. this will be denoted by Pv.

we are given the period n for this mortgage repayment which is 10 years but its stated that this individual will pay monthly so the period of payments n is 10 x 12 =120 payments will be done.

the interest rate is also given as 7%which is not adjusted over the periodic payments so i is 7%/12 thereafter we find the monthly payments which will be denoted by C in the present value formula :

$Pv = C[(1-(1+i)^-n)/i]$ then we substitute the above mentioned values

$40000=C[(1-(1+(7%/12))^-120)/(7%/12)] then we divide both sides by the value that multiplies C to solve for C the monthly payments.

$40000/[(1-(1+(7%/12))^-120)/(7%/12)] = C, then compute on calculator.

therefore C the montly payments is $464.44

we use the present value annuity as it is a series of periodic payments in the futer for a value given now.