chapter 10 nominal Flashcards
Which of the following statements regarding constant payment mortgages is TRUE?
- There are only three basic financial components in all constant payment mortgages: amortization period, nominal rate of interest, and the loan amount.
- Constant payment mortgages are repaid by equal and consecutive instalments that include principal and interest.
- If a mortgage payment frequency and interest rate compounding frequency are both monthly, an interest rate conversion is required for mortgage finance calculations.
- At the end of the amortization period, a constant payment mortgage’s future value is always equal to 10% of the loan’s face value.
Correct Answer: 2
Option (2) is correct because constant payment mortgages are repaid by equal periodic payments that occur in consecutive instalments including the principal amount and interest. Option (1) is incorrect because there are four basic financial components in all constant payment mortgages: loan amount, nominal rate of interest, amortization period, and payment. Option (3) is incorrect because when the mortgage payment frequency and interest rate compounding frequency are the same (monthly in this case), an interest rate conversion is NOT required for mortgage finance calculations. Option (4) is incorrect because at the end of the amortization period, a constant payment mortgage’s future value is equal to zero. This is because constant payment mortgages are always completely paid off at the end of the amortization period.
Which of the following nominal and periodic interest rates is NOT equivalent to a periodic interest rate of iq = 2.22%?
j2 = 8.978568%
j12 = 8.815087%
imo = 0.765009%
iw = 0.169044%
Correct Answer: 3
Option (3) is correct because the monthly rate of 0.765009% is not equivalent. To compare the rates, it is necessary to convert the quarterly periodic rate of 2.22% to the corresponding nominal or periodic rates.
Option 1
PRESS
DISPLAY
2.22 × 4 = ⬛ NOM%
8.88
4 ⬛ P/YR
4
⬛ EFF%
9.180105
2 ⬛ P/YR
2
⬛ NOM%
8.978568
Options 2 and 3
PRESS
DISPLAY
2.22 × 4 = ⬛ NOM%
8.88
4 ⬛ P/YR
4
⬛ EFF%
9.180105
12 ⬛ P/YR
12
⬛ NOM%
8.815087 (j12)
÷ 12 =
0.734591 (imo)
Option 4
PRESS
DISPLAY
2.22 × 4 = ⬛ NOM%
8.88
4 ⬛ P/YR
4
⬛ EFF%
9.180105
52 ⬛ P/YR
52
⬛ NOM%
8.790288
÷ 52 =
0.169044
Harwinder and Suki have recently moved to Victoria because of job promotions. After renting for several months, they have bought a house just outside the city centre. Harwinder and Suki financed the purchase with a $425,000 mortgage at an interest rate of 4.99% per annum, compounded semi-annually, amortized over 25 years with a 5-year term and monthly payments.
What is the monthly payment?
- $2,469.40
- $2,790.49
- $2,151.49
- $2,520.43
Correct Answer: 1
Option (1) is correct because the monthly payment is $2,469.40. Payments are made monthly, so the given nominal rate with semi-annual compounding (j2 = 4.99%) must be converted to a j12 rate. Then the monthly payment can be calculated.
PRESS
DISPLAY
4.99 ⬛ NOM%
4.99
2 ⬛ P/YR
2
⬛ EFF%
5.05225
12 ⬛ P/YR
12
⬛ NOM%
4.938902
425000 PV
425,000
25 × 12 = N
300
0 FV
0
PMT
–2,469.402346
Alex Ovichken is applying for mortgage financing in order to purchase a hockey rink. What is the maximum loan allowable (rounded to the nearest dollar), given payments of $4,000 per month, an interest rate of 5% per annum, compounded annually, and an amortization period of 20 years?
- $688,245
- $611,774
- $656,101
- $671,876
Correct Answer: 2
Option (2) is correct because the maximum allowable loan Alex could receive is $611,774, rounded. The interest rate must first be converted to an equivalent nominal rate with monthly compounding and the amortization period changed to months. Then solve for PV, the maximum loan allowable.
PRESS
DISPLAY
5 ⬛ NOM%
5
1 ⬛ P/YR
1
⬛ EFF%
5
12 ⬛ P/YR
12
⬛ NOM%
4.888949
4000 +/– PMT
–4,000
20 × 12 = N
240
0 FV
0
PV
611,773.770476
A lender quotes a nominal interest rate of 6% per annum, compounded monthly (j12 = 6%). What is the equivalent nominal interest rate per annum, compounded quarterly?
6.16778%
6.34922%
6.64929%
6.03005%
Correct Answer: 4
Option (4) is correct because the equivalent rate is j4 = 6.03005%. This question requires an interest rate conversion from a j12 rate to its equivalent j4 rate.
PRESS
DISPLAY
6 ⬛ NOM%
6
12 ⬛ P/YR
12
⬛ EFF%
6.167781
4 ⬛ P/YR
4
⬛ NOM%
6.03005
Rank the following nominal and periodic rates from highest to lowest in terms of their effective annual rate:
id = 0.03%; j12 = 10.8%; iq = 2.7%; j52 = 10.5%; j2 = 10.4%
j2 = 10.4%; iq = 2.7%; id = 0.03%; j52 = 10.5%; j12 = 10.8%
j12 = 10.8%; j52 = 10.5%; id = 0.03%; iq = 2.7%; j2 = 10.4%
j12 = 10.8%; j52 = 10.5%; j2 = 10.4%; iq = 2.7%; id = 0.03%
Correct Answer: 1
Option (1) is correct because it gives the correct order of the nominal and periodic rates from highest to lowest in terms of their effective annual rate. To compare the various rates, they should all be converted into effective annual interest rates.
PRESS
DISPLAY
id = 0.03
.03 × 365 = ⬛ NOM%
10.95
365 ⬛ P/YR
365
⬛ EFF%
11.570175
iq = 2.7%
2.7 × 4 = ⬛ NOM%
10.8
4 ⬛ P/YR
4
⬛ EFF%
11.245326
j2 = 10.4%
10.4 ⬛ NOM%
10.4
2 ⬛ P/YR
2
⬛ EFF%
10.6704
j12 = 10.8%
10.8 ⬛ NOM%
10.8
12 ⬛ P/YR
12
⬛ EFF%
11.350967
j52 = 10.5%
10.5 ⬛ NOM%
10.5
52 ⬛ P/YR
52
⬛ EFF%
11.059303
