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Federer Vaaler - Mathematical Interest Theory 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 1 / 19

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

Question
Points
1 2 3 4 5 6 7 8 9 10
1/3 –/1 0/1 –/4 0/1 –/3 –/2 –/1 –/2 –/1
Total
1/19 (5.3%)
  • Instructions

    Mathematical Interest Theory, by Leslie Jane Federer Vaaler and James Daniel, gives students an introduction of how investments grow over time. This textbook is written for anyone who has a strong high school algebra background and is interested in being an informed borrower or investor. The content is suitable for a mid-level or upper-level undergraduate course or a beginner graduate course. Through partnership with the Mathematical Association of America, WebAssign is pleased to offer online question content with instant feedback from this title. All questions include reading links to the eBook for an integrated student experience.

    Question 1 is a multi-part question that has a student find an equation of value, then use that equation to calculate dollar-weighted annual yields.

    Questions 2 and 10 utilize the calcPad so students can easily enter any correct form of the complicated functions.

    Question 3 gives the student the option to enter more than one interest rate in the case that there are multiple correct answers. Note that this particular question has only one correct answer.

    Question 4 is a multi-part question that ultimately has a student find equations for the nominal discount rate.

    Questions 5 and 7 require calculus knowledge to answer correctly.

    Question 9 steps a student through an alternate proof for the given formula.

    View the complete list of WebAssign questions available for this textbook.

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1. 1/3 points  |  Previous Answers FVIntTheory2 2.6.001. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 0/1 /1
1/5 1/5 0/5
Total
1/3
 
Sandra invests $10,832 in the Wise Investment Fund. Three months later her balance has grown to $11,892 and she deposits $2,000. Two months later her fund holdings are $14,299 and she withdraws $7,000. Two years after her initial investment, she learns that her holdings are worth $12,556.
(a)
Write an equation of value involving the exact dollar-weighted annual yield i over the two-year period. (Use the time zero equation of value.)
12556(1 + i)2 =
10832+2000·(1+i)(14)7000·(1+i)(512)
Correct: Your answer is correct.
(b)
Compute the approximate dollar-weighted annual yield over the investment period using the following formula. (Round your answer to two decimal places.)
j  
I
A
Ct(1 t)
t is in (0, 1)
j Incorrect: Your answer is incorrect. %
Compute the approximate dollar-weighted annual yield over the investment period again using the following formula. (Round your answer to two decimal places.)
j  
I
1
2
A
1  
1
2
B  
1  
1
2
I
 = 
2I
A + B 1
j %

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2. /1 points FVIntTheory2 2.7.001. My Notes
Question Part
Points
Submissions Used
1
/1
0/5
Total
/1
 
On January 1, 1988, Antonio invests $9,300 in an investment fund. On January 1, 1989 his balance is $10,800 and he deposits $2,600. On July 1, 1989 his balance is $14,700 and he withdraws $1000. On January 1, 1992 his balance is $P. Express his annual time-weighted yield
(itw)
as a function of P.
itw =

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3. 0/1 points  |  Previous Answers FVIntTheory2 1.7.007. My Notes
Question Part
Points
Submissions Used
1
0/1
1/5
Total
0/1
 

problem

You have two options to repay a loan. You can repay $6,000 now and $2,880 in one year, or you can repay $9,600 in 6 months. Find the annual effective interest rate(s) i at which both options have the same present value. (Enter your answers as a comma-separated list.)
ssss
Incorrect: Your answer is incorrect. %

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4. /4 points FVIntTheory2 1.10.007. My Notes
Question Part
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1 2 3 4
/1 /1 /1 /1
0/5 0/5 0/5 0/5
Total
/4
 
Let m be a positive real number. Suppose interest is paid once every m years at a nominal interest rate
i(1/m).
This means that the borrower pays interest at an effective rate of
i(1/m)
1
m
 = mi(1/m)
per m year period.
(a)
Find an expression for
i(1/m)
in terms of i.
i(1/m)
=
(b)
If
i(2/5) = 0.1,
find i. (Round your answer to two decimal places.)
i = %
(c)
Define
d(1/m)
to be the nominal discount rate payable once every m years. This means that the borrower pays discount at an effective rate of
d(1/m)
1
m
 = md(1/m)
per m year period.
Find a formula that gives
d(1/m)
in terms of
i(1/m).
d(1/m) =
Find a formula that gives
d(1/m)
in terms of d.
d(1/m) =

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5. 0/1 points  |  Previous Answers FVIntTheory2 1.R.009. My Notes
Question Part
Points
Submissions Used
1
0/1
1/5
Total
0/1
 
Calculus is needed.
Suppose that
δt
2
t 1
for
2 t 8.
For
2 n 7,
let
f(n) = in + 1 + 1.
Write a simple formula for
f(n).
f(n) =
3435
Incorrect: Your answer is incorrect.

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6. /3 points FVIntTheory2 1.12.008. My Notes
Question Part
Points
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1 2 3
/1 /1 /1
0/5 0/5 0/5
Total
/3
 
(a)
Fund I grows according to simple interest at rate r. Find the force of interest
δt(I)
acting on fund I at time t.
δt(I) =
(b)
Fund D grows according to simple discount at rate s. Find the force of interest
δt(D)
acting on fund D at time t.
δt(D) =
(c)
Suppose
r > s.
Find all t such that
δt(I) = δt(D).
t =

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7. /2 points FVIntTheory2 1.R.004. My Notes
Question Part
Points
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1 2
/1 /1
0/5 0/5
Total
/2
 
Calculus is needed.
(a)
Express
d
dδ
 v
as a function of d. (Assume compound interest.)
(b)
Express
d
dv
 δ
d
di
 d
as a function of d. (Assume compound interest.)

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8. /1 points FVIntTheory2 1.3.005. My Notes
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1
/1
0/5
Total
/1
 

problem

It is known that for each positive integer k, the amount of interest earned by an investor in the k-th period is k. Find the amount of interest earned by the investor from time 0 to time n, n a fixed positive integer.

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9. /2 points FVIntTheory2 4.3.007. My Notes
Question Part
Points
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1 2
/1 /1
0/5 0/5
Total
/2
 
Use the following fact to obtain an alternate proof of the formula
a
ni
(m)
1 vn
m[(1 + i)1/m 1]
.
The expression
1
m
a
nmJ
gives the present value of an annuity that pays
1
m
at the end of each m-th of an interest period, for a total of 1 per interest period. Here
J = (1 + i)1/m 1 = 
i(m)
m
is the interest rate for the annuity-payment period
According to the given fact and the equation
a
ni
1 vn
i
,
a
ni
(m)
1
m
a
nmJ
1
m
1  
nm
 
J
.
But
J = (1 + i)1/m 1
and
(1 + J)nm
n
 
.
Therefore,
a
ni
(m)
1
m
1 (1 + J)nm
J
 = 
1 vn
m[(1 + i)1/m 1]
.

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10. /1 points FVIntTheory2 4.2.007. My Notes
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/1
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/1
 
A perpetuity paying $3,000 at the beginning of each two years has the same present value as another perpetuity with level payments, this one having payments at the end of each three years. Express the level payment amount of the second perpetuity, P, as a function of the annual effective interest rate i.
P =

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