Question

John has bought a residential flat in Mong Kok at a price of $6 million. He has applied for a fully-amortizing mortgage loan from a bank for 25 years, and the interest rate for the loan was based on a composite: “Prime rate minus 2.5%”. Suppose the current prime rate and the maximum loan-to-value ratio are 5.5% and 60% respectively.

1. How much does John borrow from the bank and what is his monthly payment. (3 marks)

2. If the prime rate remains constant for the entire 25-year term, what will be John’s total payment over these 25 years? Out of this total, how much is the interest? (4 marks)

3. If there is no change in the prime rate, what is the outstanding loan balance if the loan is repaid by John at the end of year 7? (3 marks)

4. If the prime rate rises to 8% at the end of the third year, and if there is a 2% cap on expense in the mortgage contract. Find John’s new monthly payments starting from Year 4? (5 marks)

5. Compare (a) and (d), what is the percentage change in John’s monthly payments? (2 marks)

6. Discuss an advantage of using “cap”. (3 marks)

Answer 1

Given, cost of residential flat= $6 Million

Maximum Loan-to- value ratio= 60%

Therefore, amount borrowed= $6Million*60% = $3.6 Million

Interest rate is given as Prime rate minus 2.5%

Current Prime Rate= 5.5%   Therefore, interest rate on loan= 5.5%-2.5% = 3%

Tenure of the loan= 25 years

Monthly payments of loan = $ 17,071.61   calculated as follows:

A B C D 1 Monthly payments of fixed rate loan. Payments at the end of each month 3 Monthly payments (PMT) 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 $ Given that 9 Principal (loan amount) (P)= 3,600,000 No. of years (N)= 10 Rate of interest (% p.a)=R= 3 No. of months (n)= 25 300 12 Calculations: 13 14 Interest rate per month in decimals (r )= 15 No. of months (n)= 16 17 18 Formula Cell reference Value R/(100*12) D10/(100*12) 0.0025 N*12 G9*12 300 (1+r)= 1+G14 1.0025 (1+r)^n= G164610 2.11501956 [(1+r)^n]-1= G17-1 1.11501956 P*r*(1+r)^n= D9*G14*G17 19035.176 [P*r*(1+r)^n]/[(1+r)^n)-1 G19/618 17071.6073 Rounded to $17,071.61 19 20 Monthly payments (PMT)= 21 དཀ

If the Prime rate remains constant over the 25 years tenure,

Total payment over 25 years= Monthly payment*25 years*12 = $ 17,071.61*25*12 = $5,121,482.19

Out of this total, Principal= $3,600,000

Therefore, amount of interest out of the total payment= $5,121,482.19 - $3,600,000 = $1,521,482.19

If there is no change in interest rate, outstanding balance in loan at the end of 7 years= $2,846,580.68

Relevant portion of the amortization schedule is appended below:

Shedule of amortization Month Beginning Monthly Monthly Interest Principal End balance interest Payments component Component balance rate =Col (2)*(3) =Col (4)-(5) Col (2)-(6) (1) (2) (3) (4) (5) (6) (7) 1 3600000 0.0025 17071.61 9000 8071.61 3591928.39 2 3591928.39 0.0025 17071.61 8979.820982 8091.79 3583836.61 83 2866416.57 84 2856511.01 85 2846580.68 0.0025 0.0025 0.0025 17071.61 7166.041428 17071.61 7141.277513 17071.61 7116.451689 9905.57 9930.33 9955.16 2856511.01 2846580.68 2836625.52

Balance at the end of 3 years= $3,296,341.61

Relevant portion of the amortization schedule is appended below:

Shedule of amortization Month Beginning Monthly Monthly interest Principal End balance interest Payments component Component balance rate =Col (2)*(3) =Col (4)-(5) Col (2)-(6) (2) (3) (5) (6) (7) 1 3600000 0.002517071.61 9 000 8071.61 3591928.39 2 3591928.39 0 .002517071.61 8979.820982 8091.79 3583836.61 (4) 35 3313937.11 36 3305150.34 37 3296341.61 0.0025 0.0025 0.0025 17071.61 8284.842767 17071.61 8262.875856 17071.61 8240.854027 8786.76 8808.73 8830.75 3305150.34 3296341.61 3287510.86

New Prime rate= 8% (with a cap of 2%)

New interest rate= 8%-2.5%, subject to maximum of previous rate (3%) plus cap of 2%

Therefore, new interest rate=8%-5.5%= 5.5% but limited to 5%

Monthly payments from Year 4 = $20,611.39   Calculated as follows:

22 264 А в ср E 1 Monthly payments of fixed rate loan. 2 Payments at the end of each month 3 Monthly payments (PMT) 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) 7 All amounts in $ 8 Given that 9 Principal (loan amount) (P)= 3,296,341.61 No. of years (N)= 10 Rate of interest (% p.a)=R= 5 No. of months (n)= 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per month in decimals (r )= R/(100*12) D10/(100*12) 0.004166667 15 No. of months (n)= N*12 G9*12 (1+r)= 1+G14 1.004166667 17 (1+r)^n= G164G10 2.99730838 18 [(1+r)^n]-1= G17-1 1.99730838 19 P*r*(1+r)^n= D9*G14*G17 41167.30138 20 Monthly payments (PMT)= [P*r*(1+r)^n]/[(1+r)^n]-1 G19/618 20611.3897 21 Rounded to $ 20,611.39 264 16 22

Monthly payments of original loan as per part (a) = $17,071.67

Monthly payments after increase in interest rate (d) = $20,611.39

Percentage change in monthly payment= ($20,611.39 - $17,071.67)/$17,071.67= Increase by 20.7345%

Rate cap has helped in limiting the interest rate at 5%, increase by the cap of 2% only though the actual increase in benchmark Prime Rate is by 8%-5.5%= 2.5%.