Question

Adam Wilson just purchased a home and took out a $250,000 mortgage for 30 years at 8%, compounded monthly.

a. How much is Adam’s monthly mortgage payment?

b. How much sooner would Adam pay off his mortgage if he made an additional $100 payment each month? The financial tables in Appendix A are not sufficiently detailed to do parts (c) and (d).

c. Assume Adam makes his normal mortgage payments and at the end of five years, he refinances the balance of his loan at 6%. If he continues to make the same mortgage payments, how soon after the first five years will he pay off his mortgage?

d. How much interest will Adam pay in the 10th year of the loan i. he does not refinance ii. If he does refinance

Answer 1

Part (a):

Monthly payments= $ 1,834.41 Calculated as follows:

Part (b):

Number of months required to repay the loan (if payments are increased by $100)

= 298 (Rounded to nearest whole month)

Number of months as per original plan= 360

Therefore, the loan will be closed sooner by 360-298 = 62 months.

Calculation of revised period using NPER function of Excel as follows:

Part (c):

Amount to be refinanced is the present value of future (unpaid) installments treating it as ordinary annuity.

Number of future installments= 360- 60 = 300

Amount to be refinanced= $237,674.64 Calculated as PV of annuity as follows

Number of months required to repay the loan (if payments are retained at $1,834.41)

= 209 (Rounded to nearest whole month)

Number of remaining months as per original plan= 300

Therefore, the loan will be closed sooner by 300-209 = 91 months.

Calculation of revised period using NPER function of Excel as follows:

Part (d):

Interest paid in 10th year of the loan (109th through 120th month):

(i ) If not refinanced: $17,732.68

Relevant portion of amortization schedule as follows:

(ii ) If refinanced, monthly payments will be $   1,531.34 as follows:

With the revised monthly payments, Interest paid in 10th year of the loan from beginning (109th through 120th month) ie., 61 through 72 months of new loan=$12,669.51

Relevant portion of amortization schedule of the new loan as follows: