Statistic, Finance Flashcards
Here are 14 numbers. 235 218 266.5 298 222 246 264 255 274 261 277 214 256 239 What is the standard deviation?
24.3. Once you have calculated the mean, enter g s Answer is 24.30.
What would a $15,000 CD be worth after four years?
$15,000 x 1.411582 = $21,173.73
What if you deposited $6,000 per year for eight years; at which time your daughter was going off to college. How much will you have saved, at 9% interest?
$66,170.84
Column 2
$6,000 x 11.028474 = $66,170.84
If I’ll need $20,000 to replace the roof on my building 12 years from now, how much do I have to put aside every year in a replacement reserve account with 9% interest?
Go to column 3 and find the factor for 12 years. OK, now multiply that factor (.049651) by $20,000. The answer is $993.02.
How much do I have to discount a $50,000 bond to receive a 9% return over 10 years?
Find the 10 year factor in column 4 (.422411) and multiply it by $50,000. The answer is $21,121.
What’s it worth today, to buy a mortgage that will give me annual payments of $8,938 for the next 10 years, if I want a 9% return?
Find the column 5 factor (6.417658) and multiply by $8,938. The answer is $57,361.
The capitalization rate for debt; the ratio of the annual debt service to the principal amount of the mortgage loan. The mortgage capitalization rate (Rm) is equivalent to the periodic (monthly, quarterly, annually) mortgage constant times the number of payments per year on a given loan on the day the loan is initiated.
defines
Mortgage Cap Rate
Rm =
Mortgage Cap Rate
What is the Rm for a loan with 9% annual interest for 15 years?
Look in Column 6 and the answer that pops out is .124059.
.133567 is the mortgage constant for a 9% mortgage for _____ years?
13 years
What would the annual payments be on a $180,000 mortgage for 10 years at 9% interest?
Find the factor (.155820) and multiply by $180,000. The answer is $28,047.60
How much do I have to put aside each year, at 7% interest, to accumulate $9,000 to replace a roof in eight years?
f CLEAR FIN
[g] [BEG]
8n
7i
9000 CHS FV
PMT
819.82
Our homeowner’s association will need $50,000 in nine years to replace the swimming pool. How much needs to be set aside in a reserve fund each year if we can invest it at 5.5%?
f CLEAR FIN
[g] [BEG]
9n
5.5 i
50000 CHS FV PMT
4,210.40
You have now performed a calculation of a column 3 function of the six functions of a dollar. You calculated a sinking fund factor - the amount per period which will grow, with compound interest, to $1.
What’s the value today of the right to receive $5,000 in five years, discounted at 8%?
f CLEAR FIN
5n
8i
5000 CHS FV
PV
3,402.92
What is the worth today of a mortgage that will give me annual payments of $10,674.12 for 14 more years, discounted at 8% interest?
f CLEAR FIN
14 n
8i
10674.12 CHS PMT
PV
87,999.97
If we have a mortgage in the amount of $123,000 with annual payments for 20 years, at 6% interest, how much are the annual payments?
f CLEAR FIN
20 n
6i
123000 CHS PV
PMT
10,723.70
You have performed a calculation of a Column 6 function: The installment to repay $1 with interest.
Assume an $82,000 mortgage with monthly payments for 25 years, at 8.35% interest. First let’s calculate the monthly payments.
f CLEAR FIN
25 g n
8.35 g i
82000 CHS PV PMT
652.02
Assume an $118,500 mortgage, at 6.5% with a monthly payment of $883.50. For how many years was the original mortgage written?
f CLEAR FIN
6.5 g i
118500 CHS PV
883.50 PMT
n
240
The answer is 240 - but that is the number of months. To find the number of years, we enter
12 ÷
The answer is 20 years.
Assume an $118,500 mortgage, at 6.5% with a monthly payment of $883.50. For how many years was the original mortgage written?
f CLEAR FIN
6.5 g i
118500 CHS PV
883.50 PMT
n
240
The answer is 240 - but that is the number of months. To find the number of years, we enter
12 ÷
The answer is 20 years.
Assume a 27-year mortgage with a monthly payment of $1,255.74 and a 9.2% interest rate. What was the original amount of the mortgage?
f CLEAR FIN
27 g n
9.2 g i
1255.74 CHS PMT
PV
150,000
We have a $212,750 mortgage for 30 years, and the monthly payment is $1,487.58. What is the interest rate?
f CLEAR FIN
30 g n
212750 PV
1487.58 CHS PMT
i
0.63
12 x
7.50
The real answer is that the interest rate is 7.5% per year.
You can afford payments of $750/month and have $25,000 for a down payment. The bank will give a mortgage for 30 years, at 6.8% with monthly payments. How expensive a house can you buy?
f CLEAR FIN
30 g n
6.8 g i
750 CHS PMT
PV
115,043.88
25000 +
140,043.88
With your $750, you would qualify for a mortgage of just over $115,000. Add in your down payment of $25,000 and you should be able to swing a house up to about $140,000.
Let’s assume we just took out a mortgage of $182,000 for 30 years (monthly payments) at a 6.2% interest rate. How much will we pay in interest the first year?
f CLEAR FIN
30 g n
6.2 g i
182000 CHS PV PMT
What did you get?
You should have gotten 1,114.69. This is the monthly payment.
f CLEAR FIN
6.2 g i
182000 PV
1114.69 CHS PMT
12 f AMORT
= $11,223.50 interest for year 1
xy = $-2,152.78 Principal for year 1
You have a mortgage of $112,500 written for 25 years at 7.2% monthly. However, there will be a balloon payment due at the end of year five. How much will that be?
f CLEAR FIN
25 g n
7.2 g i
112500 CHS PV
PMT
809.54
Then we leave all the information in the rest of the registers, but change the entry in the n register to five years and ask for the future value after five years.
5gn
FV
102,818.06
Therefore, the remaining balance at the end of five years of the 25-year scheduled payout, to be paid off as a lump sum balloon payment, would be $102,818.06.
We have $2,000 a month we can spend for a house. Suppose that the taxes for that house would run $3,000 per year and the insurance would be $600. You go to Lender 1 to get qualified, and she quotes you an interest rate of 6.2% for a fixed rate, 20-year loan. Let’s do the math and see how much of a mortgage you could get.
f CLEAR FIN
20 g n
6.2 g i
1700 CHS PMT PV
233,511.07
So, you could qualify for a loan of about $233,500.
Bi-weekly mortgage plans have been available for a while. Instead of making 12 monthly payments a year, you make a payment xxx
every two weeks.
Let’s run that same scenario I introduced a few pages back. What if I borrow $100,000 at 5.8% for 20 years and pay two points at closing for the privilege of getting a lower interest rate. What does this do to the lender’s yield?
They loaned me $100,000, but I immediately returned $2,000 at the closing. In essence, they only loaned me $98,000. The monthly payment of $704.94 is based on a mortgage of $100,000. So let’s see how that plays out. What will the yield be if the lender receives a payment of $704.94 against a loan of $98,000?
f CLEAR FIN
20 g n
98000 CHS PV
704.94 PMT i
.50
12 X
6.05
The yield per month is .50 (to two decimal places). When we multiply it by 12 to get the annual yield, it comes out to 6.05%. So getting two points as an up-front fee will enable the lender to average a yield of 6.05%
Suppose I sell my house and retire to Arizona. I have no immediate need for the money and hold a 20-year first mortgage of $250,000 for the buyer.
Five years later, I have some medical problems and need more money. I decide to cash in my mortgage. I find an investor who is willing to take over the loan - for the right price.
The interest rate on the loan is 6.5% and it is paid monthly. The investor reaches into his briefcase, pulls out his HP 12c, makes a few keystrokes and within 10 seconds says - “I will be happy to take that mortgage off your hands for $213,972.48.” I feel very relieved as we shake hands on the deal.
How did he arrive at that figure?
Maybe the interest rates have gone up in the last five years and the investor isn’t interested in being able to obtain only 6.5 % interest. Let’s assume the investor does not want to buy the mortgage unless he or she can get an 8% return on investment. How much would that be?
f CLEAR FIN
20 g n
6.5 g i
250000 CHS PV
PMT
1,863.93
Now, let’s calculate the value of the right to receive $1,863.93/month for 15 years, at 6.5% interest. We have all the information already in the storage registers. We just need to change the term of the loan.
15 g n
PV 213,972.80
8 gi
PV
195,043.04
Probably, our investor would round it and say - “let’s make a deal at $195,000.”
What is start rate or teaser rate.
Initial interest rate is defined as:
The original interest rate of the mortgage at the time of closing. This rate changes for an adjustable-rate
mortgage (ARM). Sometimes known as start rate or teaser rate.
For an adjustable-rate mortgage (ARM), the maximum interest rate, as specified in the mortgage note.
defines
Interest rate ceiling
With an option ARM, the buyer has various options for making the payment each month:
- Fully amortizing payment
- Interest only payment
- Minimum payment
