Download Simple interest (5.1)

Simple interest (5.1)
Find the interest. Round to the nearest cent.
1) $900 at 4% for 4 years
A) Interest = $14.40
C) Interest = $56.25
1)
B) Interest = $900.00
D) Interest = $144.00
Simple Intrest
I=Prt, $144 = 900(.04)(4)
Find the exact interest. Use 365 days in a year, and use the exact number of days in a month. Round to the nearest cent, if
necessary.
2) $3300 at 8% for 160 days
2)
A) $117.33
B) $11.73
C) $115.73
D) $11.57
Simple Intrest, Exact Number of Days
I=Prt, I = 3300(.08)(160/365), I = $115.73
Find the future value of the loan.
3) $600.00 loan at 8% for 5 months
A) $840.00
B) $620.00
C) $625.00
D) $1020.00
3)
Simple Intrest, Future Value (When the question says, "Months" use 30 days for each month.)
A = P(1 +rt), A = 600(1 + (.08)(5/12)), A = $620
Find the present value of the future amount. Assume 365 days in a year. Round to the nearest cent.
4) $19,000 for 2 months; money earns 5%
A) $18,854.11
B) $18,921.16
C) $157.02
D) $18,095.24
4)
Simple Intrest, Present Value (When the question says, "Months" use 30 days for each month.)
A
19,000
P=
, P=
, P = $18,845.11
(1 + rt)
1 + .05(60/365)
The given Treasury bill was sold in April of this year. Find (i) the price of the T-bill, and (ii) the actual interest rate paid
by the Treasury. Round dollar amounts to the nearest cent and interest rates to the nearest thousandth.
5) Three-month $5000 T-bill with discount rate 0.120%
5)
A) (i) $4998.50;
B) (i) $4998.20;
(ii) About 0.12%
(ii) About 0.144%
C) (i) $4999.85;
D) (i) $5001.50;
(ii) About 0.012%
(ii) About 0.12%
Simple Intrest
I = Prt, I = 5,000(.0012)(3/12) , I = $1.5
then subtract the intrest from the principle
5,000 - 1.5 = $4,998.50
1
Compound interest type questions (5.2)
Find the compound amount for the deposit. Round to the nearest cent.
6) $1000 at 8% compounded annually for 8 years
A) $1560.00
B) $1850.93
C) $1640.00
D) $1713.82
6)
Future Value Compound Intrest
A = P(1 + n)i, A = 1000(1 + .08)8 , A = $1850.93
Find the compound interest earned by the deposit. Round to the nearest cent.
7) $16,000 at 3% compounded annually for 13 years
A) $7496.54
B) $6240.00
C) $6812.17
D) $5760.00
7)
Future Value Compound Intrest and Subtract the Principle
A = P(1 + n)i , 16,000(1 + .03)13 - 16,000 = $7,496.54
Find the interest rate (with annual compounding) that makes the statement true. Round to the nearest tenth when
necessary.
8) $10,000 grows to $10,816.00 in 2 years
8)
A) 2.5%
B) 4.25%
C) 2%
D) 4%
Intrest from Present value to Future Value
n A
2 10,816
r=
- 1, 4% =
- 1,
P
10,000
Find the compound amount and the interest earned when the given investment has continuous compounding.
9) $11,000 at 2.3% for 8 years
9)
A) $13,024.00; $2024.00
B) $13,529.81; $2529.81
C) $13,222.17; $2222.17
D) $11,255.93; $255.93
Continuous Compounding
A = Pert , $13,222.17 = 11,000(2.71828).023(8) 13,222.17 - 11,000 = $2,222.17
Solve the problem. (Find the value of the Zero-Coupon Bond)
10) Find the face value (to the nearest thousand dollars) of the 10-year zero-coupon bond at 3.6%
(compounded semiannually) with a price of $17,498.
A) $25,000
B) $15,000
C) $25,500
D) $15,800
10)
Future Value
A = P(1 + i)n , A = 17,498(1 + .036)10, A = $24,922.17, thus it is a $25,000 face value bond.
Find the APY corresponding to the given nominal rates.
11) 5% compounded semiannually
A) 5.00%
B) 5.12%
C) 5.06%
Annual Precentage Yield
r
.05 2
rE = (1 + )m - 1, rE = (1 +
) - 1, rE = 5.06%
m
2
2
D) 5.09%
11)
Find the amount that should be invested now to accumulate the following amount, if the money is compounded as
indicated.
12) $2400 at 6% compounded annually for 7 yr
12)
A) $1691.91
B) $3608.71
C) $803.86
D) $1596.14
Present Value Compounded Intrest
A
$2,400
P=
, P=
, P = $1,596.14
n
(1 + i)
(1 + .06)7
Annuities, Future Value and Sinking Funds (5.3)
Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.
13) R = $100, i = 4% interest compounded annually for 10 years
A) $1200.61
B) $355.83
C) $1058.28
D) $3700.61
13)
Future Value of Ordinary Annuity
(1 + i)n - 1
(1 + .04)10 - 1
S=R
, S = 100
, S = $1200.61
i
.04
Find the final amount (rounded to the nearest dollar) in this retirement account, in which the rate of return on the account
and the regular contribution change over time.
14) $300 per month invested at 6%, compounded monthly, for 15 years; then $700 per month invested
14)
at 7%, compounded monthly, for 15 years.
A) About $309,119
B) About $474,476
C) About $761,369
D) About $470,432
First Part: Future value of annuity 1-15 years.
(1 + i/m)n(m) - 1
(1 + .06/12)15(12) - 1
S=R
, S = 300
, S = $87,245.61
i/m
.06/12
Second Part: Future Value Compound Intrest from the first 15 years. We have to compound this
ammount as a lump sum for the second 15 years because it is earning intrest for the last 15 years at
7%.
A = P(1 + i)n, A = 87,245.61(1 + .07/12)15(12) A = $248,558.10
Third Part: Future value of annunity 16-30 years.
(1 + i/m)n(m) - 1
(1 + .07/12)15(12) - 1
S=R
, S = 700
, S = $221,873.61
i/m
.07/12
Fourth Part: Add the caculation from part 2 and part 3 to find the total of future earnings.
248,558.10 + 221,873.61 = $ 470,431.71
Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the
following amount. Payments are made at the end of each period. The interest rate given is per period.
15) $9300; money earns 8% compounded annually; 4 annual payments
15)
A) $2063.86
B) $1585.25
C) $2864.71
D) $546.86
Future Value Regular Annunity, Solve for the payment (R)
(1 + i)n - 1
(1 + .08)4 - 1
S=R
, $9,300 = R
, R = $2,063.86
i
.08
3
Find the future value of the annuity due.
16) Payments of $500 made at the beginning of each year for 7 years at 4% compounded annually
A) $15,949.15
B) $4107.11
C) $3449.15
D) $2816.49
16)
Future Value Annunity Due
(1 + i)n+1 - 1
(1 + .04)7+1 - 1
- R, $4107.11 = 500
- 500
S=R
i
.04
Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding
period is the same as the payment period.
17) $8000; quarterly payments for 8 years; interest rate 4.1%.
17)
A) $31.45
B) $69.42
C) $210.35
D) $120.37
Future Value Annunity Due, Solve for the payment (R)
("Payments", "Future Value" are specified.)
S=R
(1 + i/m)n(m)+1 - 1
(1 + .041/4)8(4) +1 - 1
- R, $8,000 = R
- R , R = $210.35
i/m
.041/4
Annuities, Present Value and Amortization (5.4)
Find the present value of the ordinary annuity.
18) Payments of $420 made annually for 13 years at 6% compounded annually
A) $3903.90
B) $3716.79
C) $3718.13
D) $3521.20
18)
Present Value of Annuity (The ammount required to be deposited as a lump sum to equal what the
future value of a simular annunity with said payments and intrest. The terms Payments and
Present value let you know it is a Present value annunity question.)
P=R
1 - (1 + i)-n
1 - (1 + .06)-13
, P = 420
, P = $3,718.13
i
.06
Find the amount necessary to fund the given withdrawals.
19) Quarterly withdrawals of $650 for 6 years; interest rate is 4.5% compounded quarterly.
A) $13,604.87
B) $3750.93
C) $101,950.69
D) $11,952.87
19)
Present Value Annunity (Key term is "to fund", and it says "withdrawals", also the "ammount
necessary." So you need to find the ammount today, Present value, required to provide
"withdrawls" not payments. Thus, it is a Present Value Annunity question.)
P=R
1 - (1 + i/m)-n(m)
1 - (1 + .045/4)-6(4)
, P = 650
, P = $13,604.87
i/m
.045/4
Find the payment made by the ordinary annuity with the given present value.
20) $50,000 monthly payments for 45 years; interest rate is 4.6% compounded monthly.
A) $2,063,010.45
B) $14,695,906.14
C) $11,391,050.38
D) $3,792,673.35
Present Value Annunity (One knows it is an annunity, not an annunity due, it also says present
value. The wording on this type of question is not as clear as the prior question.) You may have a
simular but different answer due to rounding errors unless you keep the figures in your caculator
when caculating the answer.
P=R
1 - (1 + i/m)-n(m)
1 - (1 + .046/12)-45(12)
, P= 50,000
, P = $11,391,050.38
i/m
.046/12
4
20)
Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each
year for 20 years at the given interest rate, compounded annually).
21) $950 at 3%
21)
A) $14,644.25
B) $13,607.04
C) $14,133.63
D) $14,124.13
Present Value Annunity (Key terms are "lump sum deposited today" and it is an annunity because
you will be receiving payments of $950 per month.
P=R
1 - (1 + i)-n
1 - (1 + .03)-20
, P= 950
, P = $14,133.63
i
.03
Find the price a purchaser should be willing to pay for the given bond. Assume that the coupon interest is paid twice a
year.
22) $30,000 bond with coupon rate 4.5% that matures in 5 years; current interest rate is 6.4%.
22)
A) $22,568.96
B) $21,893.96
C) $28,268.52
D) $27,593.52
Bond Payments
I = Prt, 30,000(.045)(.5) = $675
Present Value of Annuity Payments
(1 - (1 + i/m)-n(m)
(1 - (1 + .064/2)-5(2)
P=R
, P = 675
, P = $5,699.56
i/m
.064/2
Present Value of $30,000 face value of the bond
P = A(1 + i)-n , P= 30,000(1 + .064/2)-10 P = $16,132.62
Add both the present value of the bond face and present value of annuity payments
5,699.56 + 21,893.96 = $27,593.52
Find the payment necessary to amortize the loan.
23) $9000; 6% compounded annually; 7 annual payments
A) $1449.32
B) $1830.27
C) $1627.96
D) $1612.21
Present Value Annunity, Solve for the payment (R), When it says "amortize" we can use Present
Value solving for R or use the Amortize formula listed on the formula page.
1 - (1 + i)-n
1 - (1 + .06)-7
P=R
, $9,000 = R
, R = $1,612.21
i
.06
5
23)
Answer Key
Testname: EXAM_3_STUDYGUIDE
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