**Interest Rate Determination** Mortgage loan. You borrow $100,000 for twenty ye
ID: 2819321 • Letter: #
Question
**Interest Rate Determination**
Mortgage loan.
You borrow $100,000 for twenty years at 5.25% interest on Halloween, 2017.
What is your monthly payment?
What is the principal and interest dollar amount breakouts for Nov 2017, Feb 2018, June 2018, and Dec 2018?
Assuming no late payments, how much total interest did you pay in 2018, and how much in total principal?
What is the ending Balance on Dec. 31, 2018?
Regardless of whether you used 360 or 365 days the first time, now use the other and tell me what the difference in principle pay down is between the two methods at year ends 2018?
Payday loan.
You borrow $500 to buy gifts for your children. In two weeks, you need to pay $650.
What would be your interest rate over that two week period, and what would your Annual Percentage Rate be for the year?
How much profit would the PayDay Lender make in a year if they made that same loan with the same $500 every two weeks assuming 100% collections and money out on that original $500?
If the lender had $100,000 in Capital for the entire year, and assuming 100% collections and fully loaned out, what would be the gross revenue for the lender?
Savings Account
You start a saving account with $2,000 at age 26 on your birthday of January 08. The account you found limits you to depositing $2,000 a year (which you do on your birthday), but pays 10% compounded annually.
How much money would be in your account at you birthday at age 63 when you finally cash out?
How much of that final amount would be your own money, and how much would the bank have paid you?
Explanation / Answer
Mortagage Loan
Loan amount=$100,000
Monthly interest= (5.25/12)%
Number of years=20
Number of instalments=20*12=240
Monthly Instalment
Monthly instalment = $673.84 (Using PMT function of excel)
with Rate=(5.25/12)%, Nper=240,PV=100,000
Monthly interest and Monthly Principal Amount
Monthly interest is calculated using IPMT function and Principal Amount is calculated using PPMT
With Rate=(5.25/12)%, per=1, Nper=240,PV=100,000
Principal amount for Nov 2017 = $236.34 (using PPMT)
With Rate=(5.25/12)%, per=1, Nper=240,PV=100,000
With Rate=(5.25/12)%, per=4, Nper=240,PV=100,000
Principal amount for Feb 2018 = $239.46 (using PPMT)
With Rate=(5.25/12)%, per=4, Nper=240,PV=100,000
With Rate=(5.25/12)%, per=8, Nper=240,PV=100,000
Principal amount for June 2018 = $243.68 (using PPMT)
With Rate=(5.25/12)%, per=8, Nper=240,PV=100,000
With Rate=(5.25/12)%, per=14, Nper=240,PV=100,000
Principal amount for Dec 2018 = $250.14 (using PPMT)
With Rate=(5.25/12)%, per=14, Nper=240,PV=100,000
Ending Balance
The remaining balance of a loan formula can be separated into two sections, the future value of the original loan amount and the future value of the annuity.
Therefore Ending Balance as on Dec 31, 2018 will be $96,595.42
Where
PV = $100,000
Rate (r) = 5.25%/12
No of months at with closing balance is calculated (n) = 14
P is Monthly EMI = $ 673.84
Pay Day Loan
Borrowed Amount (Principal) = $500
Amount to be returned with interest = $ 650
Time = 2 weeks
Interest Amount = $ 650 - $500 = $ 150
Rate of Interest = 30% using formula
Annual Percentage Rate (APR)= (1+ 30%)^(52/2) - 1
= 916.33%
Using formula APR = (1+ rate of interest during period) ^(year/duration of period) -1
Here,
rate of interest during period = 30%
duration of period = 2 weeks
year = 52 weeks
Mortagage Loan
Loan amount=$100,000
Monthly interest= (5.25/12)%
Number of years=20
Number of instalments=20*12=240
Monthly Instalment
Monthly instalment = $673.84 (Using PMT function of excel)
with Rate=(5.25/12)%, Nper=240,PV=100,000
Monthly interest and Monthly Principal Amount
Monthly interest is calculated using IPMT function and Principal Amount is calculated using PPMT
With Rate=(5.25/12)%, per=1, Nper=240,PV=100,000
Principal amount for Nov 2017 = $236.34 (using PPMT)
With Rate=(5.25/12)%, per=1, Nper=240,PV=100,000
With Rate=(5.25/12)%, per=4, Nper=240,PV=100,000
Principal amount for Feb 2018 = $239.46 (using PPMT)
With Rate=(5.25/12)%, per=4, Nper=240,PV=100,000
With Rate=(5.25/12)%, per=8, Nper=240,PV=100,000
Principal amount for June 2018 = $243.68 (using PPMT)
With Rate=(5.25/12)%, per=8, Nper=240,PV=100,000
With Rate=(5.25/12)%, per=14, Nper=240,PV=100,000
Principal amount for Dec 2018 = $250.14 (using PPMT)
With Rate=(5.25/12)%, per=14, Nper=240,PV=100,000
Ending Balance
The remaining balance of a loan formula can be separated into two sections, the future value of the original loan amount and the future value of the annuity.
Therefore Ending Balance as on Dec 31, 2018 will be $96,595.42
Where
PV = $100,000
Rate (r) = 5.25%/12
No of months at with closing balance is calculated (n) = 14
P is Monthly EMI = $ 673.84
Pay Day Loan
Borrowed Amount (Principal) = $500
Amount to be returned with interest = $ 650
Time = 2 weeks
Interest Amount = $ 650 - $500 = $ 150
Rate of Interest = 30% using formula
Annual Percentage Rate (APR)= (1+ 30%)^(52/2) - 1
= 916.33%
Using formula APR = (1+ rate of interest during period) ^(year/duration of period) -1
Here,
rate of interest during period = 30%
duration of period = 2 weeks
year = 52 weeks
Saving Account
Rate of Interest (Compounded Annually) = 10%
Amount Deposited yearly = $2,000
Age at which deposit started = 26 years
Age at which deposit withdrawn = 63 years
Years for which money deposited = (63 -26) = 37 years
Money is deposited at the beginning of the period
Using FV function of excel to solve Future Value (money withdrawn)
Money withdrawn = $ 7,26,086.87
Where rate = 10%, nper = 37 years, pmt = $2000, [pv] =0, [type] = 1
Amount Deposited = 37 * 2000 = $ 74,000
Amount Paid by bank = $ 6,52,086.87
Rate of Interest
10%
Age
Year for which money earns interest
Amount Deposited
Compounding Factor Formula
Compounding Factor
Amount
26
37
2000
=(1+10%)^37
34.0039
68,007.90
27
36
2000
30.9127
61,825.36
28
35
2000
28.1024
56,204.87
29
34
2000
25.5477
51,095.34
30
33
2000
23.2252
46,450.31
31
32
2000
21.1138
42,227.55
32
31
2000
19.1943
38,388.68
33
30
2000
17.4494
34,898.80
34
29
2000
15.8631
31,726.19
35
28
2000
14.4210
28,841.99
36
27
2000
13.1100
26,219.99
37
26
2000
11.9182
23,836.35
38
25
2000
10.8347
21,669.41
39
24
2000
9.8497
19,699.47
40
23
2000
8.9543
17,908.60
41
22
2000
8.1403
16,280.55
42
21
2000
7.4002
14,800.50
43
20
2000
6.7275
13,455.00
44
19
2000
6.1159
12,231.82
45
18
2000
5.5599
11,119.83
46
17
2000
5.0545
10,108.94
47
16
2000
4.5950
9,189.95
48
15
2000
4.1772
8,354.50
49
14
2000
3.7975
7,595.00
50
13
2000
3.4523
6,904.54
51
12
2000
3.1384
6,276.86
52
11
2000
2.8531
5,706.23
53
10
2000
2.5937
5,187.48
54
9
2000
2.3579
4,715.90
55
8
2000
2.1436
4,287.18
56
7
2000
1.9487
3,897.43
57
6
2000
1.7716
3,543.12
58
5
2000
1.6105
3,221.02
59
4
2000
1.4641
2,928.20
60
3
2000
1.3310
2,662.00
61
2
2000
1.2100
2,420.00
62
1
2000
1.1000
2,200.00
63
$ 74,000.00
$ 7,26,086.87
Total Amount Withdrawn
$ 7,26,086.87
Amount Deposited
$ 74,000.00
Amount Paid by Bank
$ 6,52,086.87
Rate of Interest
10%
Age
Year for which money earns interest
Amount Deposited
Compounding Factor Formula
Compounding Factor
Amount
26
37
2000
=(1+10%)^37
34.0039
68,007.90
27
36
2000
30.9127
61,825.36
28
35
2000
28.1024
56,204.87
29
34
2000
25.5477
51,095.34
30
33
2000
23.2252
46,450.31
31
32
2000
21.1138
42,227.55
32
31
2000
19.1943
38,388.68
33
30
2000
17.4494
34,898.80
34
29
2000
15.8631
31,726.19
35
28
2000
14.4210
28,841.99
36
27
2000
13.1100
26,219.99
37
26
2000
11.9182
23,836.35
38
25
2000
10.8347
21,669.41
39
24
2000
9.8497
19,699.47
40
23
2000
8.9543
17,908.60
41
22
2000
8.1403
16,280.55
42
21
2000
7.4002
14,800.50
43
20
2000
6.7275
13,455.00
44
19
2000
6.1159
12,231.82
45
18
2000
5.5599
11,119.83
46
17
2000
5.0545
10,108.94
47
16
2000
4.5950
9,189.95
48
15
2000
4.1772
8,354.50
49
14
2000
3.7975
7,595.00
50
13
2000
3.4523
6,904.54
51
12
2000
3.1384
6,276.86
52
11
2000
2.8531
5,706.23
53
10
2000
2.5937
5,187.48
54
9
2000
2.3579
4,715.90
55
8
2000
2.1436
4,287.18
56
7
2000
1.9487
3,897.43
57
6
2000
1.7716
3,543.12
58
5
2000
1.6105
3,221.02
59
4
2000
1.4641
2,928.20
60
3
2000
1.3310
2,662.00
61
2
2000
1.2100
2,420.00
62
1
2000
1.1000
2,200.00
63
$ 74,000.00
$ 7,26,086.87
Total Amount Withdrawn
$ 7,26,086.87
Amount Deposited
$ 74,000.00
Amount Paid by Bank
$ 6,52,086.87
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