The Stepford family purchased a duplex in western Sydney four years ago for $395

Question

The Stepford family purchased a duplex in western Sydney four years ago for $395,000. They paid a $15,000 deposit and financed the balance through a mortgage repayable over 25 years which required equal payments to be made at the end of each month. At that time there was an interest rate of 5.5% p.a.compounded monthly. (a) What were the original mortgage payments?

Today the Stepford family has just been advised that the interest rate is to increase to 7.0% p.a. and that interest will be compounded monthly. The family has been given the choice of two options to continue paying the mortgage. Option 1: Make higher monthly payments for the remaining 21 years. Option 2: Continue the same payments but extend the period of the loan. (b) What is the amount of each new payment under Option 1? (c) How long will it take to pay off the mortgage if Option 2 is taken? (d) By how much has the annual effective rate of interest increased?

i know how to solve question a using the pv formula, but dont know how to work the rest.

Explanation / Answer

Monthly payment = Principal Amout *[( r * (1+r)^n)/ ((1+r)^n-1)]

(a) Here, Principal amount = loan amount = 395000 - 15000 = 380000

r = monthly interest rate = 5.5%/12 = 0.4583%

n = number of repayment months = 25*12 = 300

Putting all these values in the above equation, we get Monthly payment = 2333.53

Alternately, this can also be computed using Excel's PMT function, ie.

PMT (r,n,principal amount) = PMT (0.4583%, 300, 380000) = 2333.53 (ORIGINAL PAYMENT)

(b) At 21 months, remaining payment = 380000 - 4*2333.53 = 370666 [payment for 4 months has already been made]

So, new principal amount = 370666, remaing tenure (n) = 21*12 = 252, rate = 7%/12 = 0.5833%

Putting these values in the top equation or PMT function, we get monthly payment = 2811.40

(c) The first equation can be solved to find time required, with principal amount = 370666, r = 0.5833% and monthly payment = 2333.53 (same as answer a).

Alternately, it can be calculated using excel function, NPER (rate, monthly payment, principal amount), ie. NPER (7%, 2333.53, 370666) ~= 37 years

(d) Rates given are with monthly compounding. To convert it to annual effective we do,

(1+monthly rate/12)^12 - 1

So, 5.5% monthly = (1+5.5%/12)^12 - 1 ~= 5.64%

7% = (1+7%/12)^12 - 1 ~= 7.23%

Thus, change in effective rate = 7.23 - 5.64 ~= 1.59%

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.