Non Interest Theory
1.
500 + 503 + 506+509 + … + 599 =
2.
If x2 + 5x +8 = 16, calculate x.
3.
1 + 3+9+27+…+59,049 =
Chapter 1
4.
A fund is earning 6% simple interest. The amount in the fund at time zero is
10,000. Calculate the amount at the end of the 5th year.
5.
A fund is earning 6% simple interest. The amount in the fund at the end of the 5th
year is 10,000. Calculate the amount at the end of the 10th year.
9.
Account A pays a simple rate of interest of 20%. Account B pays a compound
interest rate of 5%. What year will the annual effective interest rate for Account
A be equal to the annual effective interest rate for Account B?
13.
Calculate the present value of $2000 payable in 10 years using an annual effective
discount rate of 8%.
14.
Calculate the accumulated value at the end of 3 years of 15,000 payable now
assuming an interest rate equivalent to an annual discount rate of 8%.
15.
Calculate the accumulated value at the end of 3 years of 250 payable now
assuming an interest rate of 12% convertible monthly.
16.
Calculate the present value of $1000 payable in 10 years using a discount rate of
5% convertible quarterly.
17.
A deposit is made on January 1, 2004. Calculate the monthly effective interest
rate for the month of December 2004, if:
a. The investment earns an 4% compounded monthly;
b. The investment earns an annual effective rate of interest of 4%;
c. The investment earns 4% compounded semi-annually;
d. The investment earns interest at a rate equivalent to an annual rate of
discount of 4%;
e. The investment earns interest at a rate equivalent to a rate of discount of 4%
convertible quarterly.
f. The investment earns 4% simple interest.
18.
Investment X for 100,000 is invested at a nominal rate of interest of j, convertible
semi-annually. After 4 years, it accumulates to 214,358.88. Investment Y for
100,000 is invested at a nominal rate of discount of k, convertible quarterly. After
two years, Investment Y accumulates to 232,305.73. Investment Z for 100,000 is
invested at an annual effective rate of interest equal to j in year 1 and an annual
effective rate of discount of k in year 2. Calculate the value of Investment Z at
the end of two years.
19.
For each of the following, given A:, calculate B:.
g. A: i=0.12
B: d(12)
h. A: i(12) = 0.12
B: i(4)
(6)
i. A: d = 0.09
B: i
20.
You are given that δ = 0.05. Calculate the accumulated value at the end of 20
years of $1000 invested at time zero.
21.
You are given that δ = 0.05. Calculate the accumulated value at the end of 30
years of $1000 invested at time equal to 10 years.
22.
You are given that δ = 0.05. Calculate the amount that must be invested at the
end of 10 years to have an accumulated value at the end of 30 years of $1000.
23.
You are given that δt = t/100. Calculate the accumulated value at the end of 10
years of $1000 invested at time zero.
24.
You are given that δt = t/100. Calculate the accumulated value at the end of 15
years of $1000 invested at the end of the fifth year.
25.
You are given that δt = t/100. Calculate the present value at the end of the 10 year
of an accumulated value at the end of 15 years of $1000.
26.
On July 1, 1999 a person invested 1000 in a fund for which the force of interest at
time t is given by δt = .02(3 + 2t) where t is the number of years since January 1,
1999. Determine the accumulated value of the investment on January 1, 2000.
27.
Calculate k if a deposit of 1 will accumulate to 2.7183 in 10 years at a force of
interest given by:
j. δt = kt for 0<t<=5
k. δt = .04kt2 for 5<t<=10
28.
Christina invests 1000 on April 1 in an account earning compound interest at an
annual effective rate of 6%. On June 15 of the same year, Christina withdraws all
her money. How much money will Christina withdraw if the bank counts days:
l. Using actual/actual method (ignoring February 29th)
m. Using 30/360 method
n. Using actual/360 method
29.
Chris invests 1000 on Janaury15 in an account earning simple interest at an
annual effective rate of 10%. On November 25 of the same year, Chris withdraws
all her money. How much money will Chris withdraw if the bank counts days:
o. Using exact simple interest (ignoring February 29th)
p. Using ordinary simple interest
q. Using Banker’s Rule
30.
Ten years ago Rachel invested 10,000. Eight years ago, she invested another
10,000. Five years ago, she withdrew 12,000 to buy a car. Rachel has earned a
nominal rate of interest of 10% compounded continuously. Now Rachel wants to
buy a new BMW for 44,000. If Rachel uses all the money available in her
account, how much additional money must Rachel borrow to buy her car?
Chapter 2
6.
Nora invests 1000 at an effective annual interest rate for 10 years. After 10 years,
her investment has doubled. Calculate the annual interest rate earned by Nora.
7.
Chris deposits 10,000 in a bank. During the first year the bank credits an annual
effective rate of interest of i. During the second year, the bank credits an annual
effective rate of interest of (i-.05). At the end of two years, Chris has 12,093.75
in the bank. Calculate i.
8.
Brittany invests 5000 at 5% interest compounded annually. How long will it be
until Brittany has 15,000?
10.
Matt wants to have 1,000,000 at age 65 when he plans to retire. Matt is now 25
and can invest money at 10% annual effective interest. Calculate the amount that
Matt must invest now to achieve his goal.
11.
You are given that i = 0.0915. If the present value of 1 paid in n years plus the
present value of 3 paid in 2n years is 2.5431, calculate n.
12.
The present value of 5 payable in 10 years plus the present value of 90 payable in
20 years is 25. Calculate i.
31.
Payments of 300, 500, and 700 are made at the end of years five, six, and eight.
Calculate the point in time at which as single payment of 1500 is equivalent using
the method of equated time.
32.
Using the method of equated time, a payment of 400 at time t=2 plus a payment
of X at time t=5 is equivalent to a payment of 400+X at time t=3.125. Calculate
X.
33.
A payment of 1 is made at the end of each year 21 through 40. Calculate the
value of t using the method of equated time.
34.
Melanie invests 1000 today. What annual effective interest rate will Melanie have
to earn in order to have 2000 in 6 years?
35.
Greg invests an inheritance of $100,000 at a constant force of interest of δ. After
12 years, Greg will have $250,000. Calculate δ.
36.
Chris wants to have 6000 in 4 years. He invests 2000 now and 3000 in two years.
What annual effective interest rate must Chris earn to achieve his objective?
67.
An investment project has the following cash flows:
Year
0
1
2
3
4
5
6
Contributions
100
200
10
10
10
5
0
Returns
0
0
60
80
100
120
60
a. Calculate the Net Present Value at 15%.
b. Calculate the internal rate of return on this investment.
70.
A fund has 10,000 at the start of the year. During the year $5000 is added to the
fund and $2000 is removed. The interest earned during the year is $1000. Which
of the following are true:
i. The amount in the fund at the end of the year is $14,000.
ii. If we assume that any deposits and withdrawals occur uniformly
throughout the year, i is approximately 8.33%.
iii. If the deposit was made on April 1 and the withdrawal was made
on August 1, then i is approximately 7.74%.
(a)
(b)
(c)
(d)
(e)
Only Item i is true.
Only Item i and ii are true
Only Item i and iii are true
All three Items are true
The correct answer is not given by (a), (b), (c), or (d).
71. Which of the following are true?
i. Time weighted rates of interest will always be higher than dollar
weighted rates of interest.
ii. Dollar weighted rate of interest provide better indicators of
underlying investment performance than do time weighted rates of
interest.
iii. Dollar weighted rates of interest provide a valid measure of the
actual investment results.
(a)
(b)
(c)
(d)
(e)
Only Item ii is true
Only Item i and ii are true
Only Item ii and iii are true
All three Items are true
The correct answer is not given by (a), (b), (c), or (d).
72. A fund has 1000 at beginning of the year. Half way through the year, the fund
value has increased to 1200 and an additional 1000 is invested. At the end of the
year, the fund has a value of 2100.
a. Calculate the exact dollar weighted rate of return using compound
interest.
b. Calculate the estimated dollar weighted rate of return using the
actual timing of the contributions and simple interest.
c. Calculate the time weighted rate of return.
119. The rate of interest is 10% and the rate of inflation is 5%. A single deposit is
invested for 20 years. Let A denote the value of the investment at the end of 10
years, measured in time 0 dollars. Let B denote the value of the investment at the
end of 10 years computed at the real rate of interest. Find the ratio of A/B.
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
18,683
1.275 or -6.275
88,573
13,000
12,307.69
7.177%
12.5%
22.517 years
16th year
22,094.93
3
7.177%
868.78
19,263.17
357.69
604.62
a. 0.0033333
b. 0.0032737
c. 0.0033059
d. 0.0034076
e. 0.0033557
f. 0.0032154
200,000
a. 0.112795
b. 0.121204
c. 0.094921
2718.28
2718.28
367.88
1648.72
2718.28
535.26
1046.03
6/145 = 0.0413793
a. 1012.05
b. 1012.05
c. 1012.21
29.
a. 1086.03
b. 1086.11
c. 1087.22
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
14,346.43
6.73
240
30.5
12.246%
0.07636
6.6517%
1359.03
2059.00
5513.30
870.27
a. True
b. False
c. False
d. False
e. False
f. True
g. True
h. True
20%
3.5265%
10
1/12
1/1.4
a. Fund A = 740.12 while Fund B = 776.40
b. Lisa has 1211.54 and Heather has 1299.12
5.0805
45,582.96
1835.43
15,914.19
41,470.22
6716.79
103,778
10
2050
a. 6866.52
b. 6846.27
8394.60
a. 10.44
b. 10
60.
a. 4621.75
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
b. 5053.90
6000
38.25
45,561.83
a. 45,094.57
b. 44,518.36
216.74
160.84
a. -55.51
b. 7.49%
244.87
8977.47
C.
E.
a. 6.70%
b. 6.66%
c. 14.55%
1976.88
8863.25
8876.56
9409.16
87,724.16
69,430.92
10,000
6,500
68.06
80
74.07
8.1442%
No Answer Provided
1000
690.29
4049.66
No Answer Provided
10.89%
2050 and 3388.80
163.30 and 274.18
9040.93
-31.45
10,472.28
7.1773%
12,464.76
9,319.06
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
12,166.04
2,846.98
No Answer Provided
No Answer Provided
13.84
a. 94,031.03
b. 95,902.37
c. 1,658.44
d. 94,243.93
e. 94,244.98
f. 94,235.70
12.30% convertible semi-annually
1
4.614 convertible semi-annually
6.4828%
a. 902.88
b. 1081.11
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
a. 902.88
b. 1111.18
2000
42
60.44
0.38
0.35
8%
0.46
987.5
1
43.49
45.69
4.84%
4.72%
0.007
5.5%
5
5.92
20
5.64