Math (Annual Interest Rate) Flashcards
Sue purchased a townhouse in December 2006 for $145,000. In December 2011, it was appraised at
$260,000. In December 2013, Sue sold the townhouse for $190,000. What was the pre-tax yield on her investment expressed as an effective annual rate?
(1) 3.936807%
(2) 8.699947%
(3) 9.388291%
(4) 4.582727%
1
j1 = ?
n=7
-145,000 0 190,000
=3.93
An investor plans to pay $200,000 for a vacant lot which he feels will sell at the end of three years for
$280,985.60. What effective annual interest rate will the investor earn? (Ignore real property taxes)
(1) 14%
(2) 13%
(3) 12%
(4) 11%
3
j1 =
n=3
-200,000 0 280,985.60
=12.0%
Smiling Sue purchased a townhouse in March 2007 for $262,000. In March 2011, it was appraised at
$350,000. In March 2014, Smiling Sue sold the townhouse for $332,000. What was the pre-tax yield on her investment expressed as an effective annual rate?
(1) 6.098489%
(2) 3.440586%
(3) 5.907385%
(4) 4.717696%
2
j1 = ?
n=7
-262,000 0 332,000
=3.441%
If investors are able to double their funds in six years, what would be the effective annual rate of interest earned on those funds? Assume that you invest $100 today so that it will grow to $200 in six years.
(1) 33.333333%
(2) 20.093695%
(3) 16.666667%
(4) 12.246205%
4
j1=?
n=6
-100 0 200
=12.24
An investor has negotiated to purchase a piece of raw land for $375,000. The investor believes that the land will increase substantially in value, and that at the end of 3 years the land will sell for $483,400. What yield expressed as an effective annual rate will the investor earn on this investment?
(1) 8.832463%
(2) 9.493867%
(3) 6.664926%
(4) 7.645597%
1
j1=?
n=3
-375,000 0 483,400
=8.83
An investor plans to pay $200,000 for a vacant lot that the investor feels will sell at the end of three years for $280,985.60. What yield, expressed as an annual rate with semi-annual compounding, will the investor earn? (Assume that these are the only cash flows for this investment.)
(1) 11.660105%
(2) 11.386551%
(3) 12%
(4) There is no possible solution for this problem.
1
j1=? (needs to be converted to j2 after)
n=3
-200,000 0 280,985.60
=11.66
A seller is willing to sell his house, by way of a take-back mortgage, for $90,000. The seller demands 24 monthly payments, and payment of the outstanding balance in the amount of $75,000 with the 24th payment. The seller wishes to earn an effective annual rate of 15% on his money. What is the monthly payment required?
(1) $1,664.80
(2) $7,048.03
(3) $1,599.22
(4) $720.60
3
j1=15%
n=24
90,000 ? -75,000
=1,599.22
What will be the purchase price of a mortgage which will provide the buyer with 48 payments of $650 plus an outstanding balance of $55,858.13 at the end of 48 months, if the buyer of the mortgage requires an effective annual yield of 15%?
(1) $55,698.26
(2) $54,867.08
(3) $52,536.87
(4) $58,989.30
1
j1=15%
n=48
? -650 55,858.13
=$55,698.25
A nominal interest rate of 8% per annum, compounded semi-annually is NOT equivalent to:
(1) an effective annual rate of 8.16%.
(2) 1.98039% per quarter.
(3) 4.85006% per annum, compounded monthly.
(4) 7.84499% per annum, compounded daily.
3
A local mortgage broker arranged a mortgage in the amount of $210,000. The borrower has agreed to pay a brokerage fee in the amount of $7,200 which is to be added to the loan amount, giving a face value of
$217,200 for the loan. The mortgage bears interest at a contract rate of 4.5% per annum, compounded semi- annually. The mortgage has an amortization period and term of 20 years and calls for monthly payments.
If the mortgage is sold to an investor for $225,000 immediately after the loan is initiated, the investor will earn the following nominal interest rate, with semi-annual compounding:
(1) 4.083034%
(2) 4.162285%
(3) 4.018729%
(4) 4.124712%
1
j2 = 4.5 n= 240
217200 pmt? 0
pmt = -1369.24
j12=?
n=240
225000 -1369.24 0
j12= 4.05
THEN!! convert to J2!!! = 4.05
A borrower has proposals from four lenders to advance funds of $122,000 as a mortgage loan. Payments on each loan will be made annually.
A B C D Face Value 125,500 125,000 124,000 123,000 Amortization 8 yrs 5 yrs 7 yrs 6 yrs Rate: j2 = 6.6% 6.5% 6.75% 7%
Based on effective annual interest rates on funds actually advanced, which alternative should the borrower choose?
(1) A
(2) B
(3) C
(4) D
3
A loan contract was written for a face value of $50,000 at j2 = 10.75% with a 20-year amortization and a 5-year term. Payments were to be made monthly in the amount of $499.76 and the outstanding balance at the end of the term was $45,167.50. A brokerage fee of $2,000 was deducted from the face value, so the funds actually advanced to the borrower were $48,000. What is the effective annual rate of interest on the funds advanced?
(1) 12.257094%
(2) 11.038905%
(3) 11.618034%
(4) 10.516863%
1
j12=
n=60
48,000 -499.76 - 45,167.50
j12 to j1
=12.25
A mortgage is arranged on the following terms:
Mortgage Face Value $170,000 Funds Advanced $163,500 Interest Rate j2 = 6.5% Amortization Period 20 years Term 20 years Payments monthly, rounded up to the next higher dollar Calculate the rate of interest paid on funds advanced, expressed as an effective annual rate. (1) 7.904213% (2) 7.135321% (3) 8.196945% (4) 6.952145%
2
FINALLY!!
j2 = 6.5%
n=240
170,000 ? 0
j12 = ?
n=240
163,500 -1,252.15 0
after converting j12-j1 = 7.13
A purchaser has just agreed to a below-market vendor-supplied mortgage with a developer. The $384,000 mortgage is set at an interest rate of j2=1.95%, with monthly payments over a 30-year amortization and a 3-year term. If the developer sells the 3-year term loan immediately to a mortgage investor for $350,000, what is the mortgage investor’s yield, expressed as an effective annual rate (j1)?
(1) 5.152415%
(2) 5.695532%
(3) 4.958129%
(4) 5.385054%
4
ok seemed to work here, but the other one didnt? anyways j2=1.95 (convert) n=30X 12 384,000 -1408.25 0
j12
n36
350,000 -1408.25 osb36(354,859.13
then convert the interest to J1
=5.39
A mortgage broker has helped you set up a mortgage loan. The loan is for $350,000 at an interest rate of j12 = 4.75% and a 20-year amortization. The loan calls for monthly payments of $2,262 over a 2-year term with $327,975.95 owing at the end of 2 years.
If the lender pays the broker a fee of 2% of the funds advanced, what is the yield to lender, expressed as an effective annual rate (j1)?
(1) 3.742599%
(2) 6.002862%
(3) 4.749999%
(4) 5.251251%
1
boy this was a tough one!!!
ok the tricky part, when they say 2% of the funds, that means, the lender is lending more than the 350,000
so..
350,000 X 2% = 7000
so the total amount of the loan = 357,000
then go-
j12=?
n=24
357,000 -2,264 -327,975.95
=3.679
then convert j12 to j1 = 3.742599!!!!!
