172A Math Exam 1 10/22/10
Name: _______________________
1.
Deposit to fund: $3,000 paid on 1/1/2010
Withdrawal from fund: $1,000 on 1/1/2015
Interest accumulates at the following rates for the various periods specified:
2010 through 2012:
2013 through 2016:
2017 through 2022:
d(5) = 8%
= 7%
i(24) =6%
What is value of the fund as of 12/31/2022? Do the problem whichever way you
want. If you use the TVM functions on your calculator, fill in the boxes below.
n
i
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PMT
FV
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2.
Bank I credits interest at a continuous rate that is a function of t:
(t) = (50+10t+t2)/1000
a) $5,000 is deposited at t=2. What is the accumulated value at t=6 ?
b) What is the annual rate of simple interest earned during the investment
period?
3.
Anthony opened a savings account at Bank Z on 7/1/2010. It credits interest at
a nominal rate of 8% compounded quarterly.
He made the following deposits and withdrawals.
Deposits: 7/1/2010 $500, 7/1/2014 $200
Withdrawals: 7/1/2012 $100, 7/1/2015 $X, 7/1/2018 $865
The 7/1/2018 withdrawal emptied the account.
1) Draw a timeline of the cashflows in and out of the account
2) Calculate X to 2 decimal places, if you use the calculator functions, be
sure to show all entries
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4.
Anne and Frank each borrow $12,000 from their father.
Anne repays her loan with two payments: $6,000 in 2 years and $8,000 in 4
years
Frank prefers to make a single payment of $15,000.
When should Frank make the payment so that he and Anne will each have the
same effective interest rate?
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4.
Kristina opened a savings account on 1/1/2007 and made the following deposits:
1/1/2007: $2,500; 1/1/2012: $900
She made the following withdrawals:
1/1/2011: $700; 1/1/2015: $500
Her account balance on 12/31/2016 is $5,000
a. Show on a timeline the cash flows in and out of this account.
b. What was the effective annual rate of interest (IRR) Kristina earned in this
account from 1/1/2007 to 12/31/2016?
c. If the Bank had promised an interest rate of 5% compounded annually,
what would be the account balance on 12/31/2016?
5.
An investor pays $100,000 today for a investment that returns cash flows of
$70,000 at end of year 3 and $50,000 end at of year 4, half of year 3s cash flow
is invested in a two-year Certificate of Deposit (CD) to earn 8% per annum
effective and all of year 4s cash flow is invested in a one-year CD to earn 7%
per annum effective. All monies are withdrawn by t=5
If i = 5%, what is the Net Present Value (NPV) of this investment today?
6.
Daniel opens an account at Bank B that credits interest at i(4)=6% and deposits
$10,000
He makes the following annual withdrawals starting at t=1:
$X for 1 year, followed by $2X for 2 years, followed by $4X for 4 years
At t=8, he still has $2,500 left in his account.
Calculate X
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7.
Values of Fund:
Date
Balance
12/31/09
10,000
3/31/10
12,000
6/30/10
14,000
Deposits:
$4,000 (1/1/10);
$1,500 (1/2/10);
12/31/10
X
$2,000 (4/1/10)
Withdrawals
9/30/10
15,000
$250 (4/2/10)
The dollar-weighted rate of return for 2010 is 10%.
What is the time-weighted rate of return for 2010?
In your calculation, you can ignore the effect of one or 2 days of timing
differences. Also, for dollar-weighted calculation, you can use either simple or
compound interest.
8.
Given:
s2n =
vn
42.13229
= .49662
Solve for n
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PMT
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9.
At an annual effective interest rate of i, the PV of a perpetuity paying $15 every
2 years equals $124, with the first payment at the end of year 6.
Using the same interest rate i, calculate the PV of a perpetuity that pays $2
every quarter, with the first payment 1 year from now.
9.
Mr. Rich creates an endowment that will pay out $100,000 at the end of each
year in perpetuity. The first n payments will go to charity A and the next 2n
payments will go to Charity B, after that, all remaining payments will go to
Charity C.
The PV of Charity Cs share is $438,656 and represents one-third of the value
of the endowment.
Calculate the PV of As and Bs share respectively.
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10.
Interest is credited under the investment year Method according to the
following table:
Marcella made the following deposits:
1/1/1989 $1,000
1/1/1992 $1,500
1/1/1993 $500
a) What is the value of her account on 12/31/1994
b) What is level annual effective rate of interest she earned from 1/1/89 to
12/31/94?