Question 1

You have some money on deposit in a bank account which pays a nominal (or quoted)rate of 8.0944 percent,but with interest compounded daily (using a 365 day year).Your friend owns a security which calls for the payment of $10,000 after 27 months.The security is just as safe as your bank deposit,and your friend offers to sell it to you for $8,000.If you buy the security,by how much will the effective annual rate of return on your investment change?
A) 1.87%
B) 1.53%
C) 2.00%
D) 0.96%
E) 0.44%

Accepted Answer

Step 1 - Compute the effective rate for the bank account.
Effective interest rate = 11ea7fdb_fc25_27a4_a768_692d7af2065a_TB2902_00 - 1
Effective interest rate = 11ea7fdb_fc25_27a5_a768_23ccf6f33ad4_TB2902_00 - 1 = 8.43%
Step 2 - Compute the nominal rate for the security.
Nominal interest rate = 11ea7fdb_fc25_27a6_a768_c1d03b2dfe5c_TB2902_00 - 1
Nominal interest rate = 11ea7fdb_fc25_4eb7_a768_af48d43fd47b_TB2902_00 - 1 = 9.96%
Step 3 - Convert the nominal rate into an effective rate.
Effective interest rate = 11ea7fdb_fc25_4eb8_a768_91e9cdc61d3a_TB2902_00 - 1 = 10.47%
Step 4 - Compare the two rates.
10.47% - 8.43% ≈ 2%

Question 2

Joe expects to receive a gift of $1,000 when he graduates one year from today.Joe can invest his gift at 6% compounded annually and he would like to use the funds in four years to purchase an engagement ring for Mabel.How much will he have in four years to spend on a ring?
A) $1,191.02
B) $1,180.00
C) $1,200.00
D) $1,262.48
E) $1,175.00

Accepted Answer

FV = PV × 11ea7fdb_fc24_161b_a768_19dbdd1d5561_TB2902_00 FV = 1,000 × (1.06 11ea7fdb_fc24_161c_a768_eb0a4b21d3f5_TB2902_00 = $1,191.02
Using a financial calculator:
N = 3, I/Y = 6, PV = -1000, PMT = 0, cpt FV = $1,191.02

Question 3

The Vanguard Windsor II mutual fund had a net asset value of $15.07 at the beginning of 1992 and $24.04 at the beginning of 1997.What was the approximate average annual growth rate in this measure over this period? (Round to the nearest whole number)
A) 60%
B) 8%
C) 10%
D) 18%
E) 15%

Accepted Answer

i = 11ea7fdb_fc26_121a_a768_f53da7f99861_TB2902_00 - 1
i = 11ea7fdb_fc26_121b_a768_2f031a1e1809_TB2902_00 - 1 = 9.79%
Using a financial calculator:
N = 5, PV = -15.07, PMT = 0, FV = 24.04, cpt I/Y = 9.79%

Question 4

Casey has $1,000 to invest and would like to buy a $3,000 jet-ski in four years.If interest is compounded annually,what interest rate will she have to receive to reach her goal?
A) 300%
B) 16%
C) 32%
D) 3%
E) 7%

Accepted Answer

i = 11ea7fdb_fc25_c3f4_a768_f129c0a5f607_TB2902_00 - 1
i = 11ea7fdb_fc25_c3f5_a768_8d3a4123b71e_TB2902_00 - 1 = .3161 or 32%
Using a financial calculator:
N = 4, PV = -1,000, PMT = 0, FV = 3,000, cpt I/Y = 31.61 or 32%

Question 5

Gary has $1,400 to invest with the goal of having $4,000 available to purchase a used car.If he can earn 12% compounded semiannually on his investment,how long will he have to wait to acquire his car?
A) Eighteen years
B) Nine years
C) Eighteen months
D) Nine months
E) Four years

Accepted Answer

Using a financial calculator:
I/Y = 6, PV = -1400, PMT = 0, FV = 4000, cpt N = 18 semiannual periods, or nine years

Question 6

When you turned 20,you deposited $1,500 into an account paying interest that is compounded quarterly.You just turned 30,and there is now $2,233.30 in the account.What nominal annual interest rate is the account paying?
A) 1.00%
B) 4.00%
C) 4.06%
D) 16.24%
E) 3.75%

Accepted Answer

i = 11ea7fdb_fc25_75cb_a768_79b4dd8016d1_TB2902_00 - 1
i = 11ea7fdb_fc25_75cc_a768_2f5e7285d74a_TB2902_00 - 1 = 4.06% (effective)
Effective interest rate = 11ea7fdb_fc25_75cd_a768_17ff4af21ac7_TB2902_00 - 1
.046 = 11ea7fdb_fc25_9cde_a768_9929716e7b1e_TB2902_00 - 1
1.046 = 11ea7fdb_fc25_9cdf_a768_6198fc7c0b86_TB2902_00 1.0099 = 11ea7fdb_fc25_9ce0_a768_b164ab46e0f9_TB2902_00 .0099 = 11ea7fdb_fc25_9ce1_a768_f55c686deeea_TB2902_00 i = 4%
Using a financial calculator:
N = 40, PV = -1,500, PMT = 0, FV = 2,233.30, cpt I/Y = 1 1 × 4 = 4.00%

Question 7

If a US Saving bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100,what is the annual rate of return on the bond?
A) 5 percent
B) 6 percent
C) 7 percent
D) 8 percent
E) 4 percent

Accepted Answer

i = 11ea7fdb_fc25_eb06_a768_e1a90ef649ce_TB2902_00 - 1
i = 11ea7fdb_fc25_eb07_a768_cdc5e43e1889_TB2902_00 - 1 = 5%
Using a financial calculator:
N = 25, PV = -29.50, PMT = 0, FV = 100, cpt I/Y = 5%

Question 8

How much will you need in 30 years to have the same purchasing power that $150 has today,if inflation averages 4% per year?
A) $486.51
B) $180.00
C) $120.00
D) $169.08
E) $330

Accepted Answer

FV = PV × 11ea7fdb_fc24_d97d_a768_354ff4cd596b_TB2902_00 FV = 150 × (1.04 11ea7fdb_fc24_d97e_a768_bb12be39847a_TB2902_00 = $486.51
Using a financial calculator:
N = 30, I/Y = 4, PV = -150, PMT = 0, cpt FV = $486.51

Question 9

$100 is received at the beginning of year 1,$200 is received at the beginning of year 3.If these cash flows are deposited at 12 percent,their combined future value at the end of year three is: (Round to the nearest whole dollar)
A) $672
B) $536
C) $427
D) $364
E) $336

Accepted Answer

Step 1 - Calculate the future value of each cash flow.
FV = PV × 11ea7fdb_fc25_008f_a768_b978517963ba_TB2902_00 11ea7fdb_fc25_0090_a768_25948cc030cd_TB2902_00 = 100 × 11ea7fdb_fc25_0091_a768_e9fec1437c32_TB2902_00 = 140.49 11ea7fdb_fc25_0092_a768_49901a13a360_TB2902_00 = 200 × 11ea7fdb_fc25_0093_a768_9f3886fb0922_TB2902_00 = 224
Step 2 - Add the values together.
140.49 + 224 = 364.49 or $364

Question 10

A firm's stock price is $25 per share and is expected to grow at a 5% compound annual rate.What should the stock price per share be in five years?
A) $26.25
B) $125.00
C) $75.00
D) $31.91
E) $69.66

Accepted Answer

FV = PV × 11ea7fdb_fc25_c3f2_a768_9547d75b59e0_TB2902_00 FV = 25 × 11ea7fdb_fc25_c3f3_a768_c9b84ad1427c_TB2902_00 = $31.91
Using a financial calculator:
N = 5, I/Y = 5, PV = -25, PMT = 0, cpt FV = $31.91

Question 11

What is the effective interest rate of 4% compounded quarterly?
A) 4.60%
B) 4.80%
C) 4.16%
D) 4.06%
E) 4.76%

Accepted Answer

Effective interest rate = 11ea7fdb_fc24_b26b_a768_0ba40a0e67ec_TB2902_00 - 1
Effective interest rate = 11ea7fdb_fc24_d97c_a768_93c0f58029bc_TB2902_00 - 1 = 4.06%

Question 12

If interest rates are 5%,which of the following will produce the largest amount of money in four years?
A) $500 earning simple interest
B) $400 with interest compounded annually
C) $300 with interest compounded semiannually
D) $100 with interest compounded quarterly
E) $25 with interest compounded monthly

Accepted Answer

FV = PV × 11ea7fdb_fc24_6441_a768_19c195e51661_TB2902_00 11ea7fdb_fc24_8b52_a768_d10f462d70aa_TB2902_00 = 500 × .05 × 4 + 500 = $600 11ea7fdb_fc24_8b53_a768_67184535cfb1_TB2902_00 = 400 × 11ea7fdb_fc24_8b54_a768_0598527abd47_TB2902_00 = $486.20 11ea7fdb_fc24_8b55_a768_15ba2ca496cc_TB2902_00 = 300 × 11ea7fdb_fc24_8b56_a768_bf286e8f357d_TB2902_00 = $365.52 11ea7fdb_fc24_8b57_a768_a99e0f246502_TB2902_00 = 100 × 11ea7fdb_fc24_b268_a768_436544fd8b4c_TB2902_00 = $121.99 11ea7fdb_fc24_b269_a768_7db7a5500bcd_TB2902_00 = 25 × 11ea7fdb_fc24_b26a_a768_0333e47b2748_TB2902_00 = $30.52

Question 13

If $100 is placed in an account that earns a nominal 4%,compounded quarterly,what will it be worth in 5 years?
A) $122.02
B) $105.10
C) $135.41
D) $120.90
E) $117.48

Accepted Answer

FV = PV × 11ea7fdb_fc25_4eb9_a768_3d3df2238445_TB2902_00 FV = 100 (1 + ( 11ea7fdb_fc25_75ca_a768_619dbfa0ba83_TB2902_00 ))²⁰ = $122.02 On a financial calculator: N = 20, I/Y = 1, PV = -100, cpt FV = $122.02

Question 14

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is:
A) $253
B) $252
C) $158
D) $134
E) $248

Accepted Answer

FV = PV × 11ea7fdb_fc23_c7f9_a768_e566bc3e023e_TB2902_00 FV = 200 × (1.04 11ea7fdb_fc23_ef0a_a768_1d680490a5e9_TB2902_00 = $253.06
Using a financial calculator:
N = 6, I/Y = 4, PV = -200, PMT = 0, cpt FV = $253.06

Question 15

Kayla hopes to purchase a new car in five years.If she deposits $10,000 today in an account that pays 7% compounded quarterly,how much will she be able to spend on the new car in five years?
A) $14,025.52
B) $10,700.00
C) $14,147.78
D) $13,500.00
E) $15,000.00

Accepted Answer

FV = PV × 11ea7fdb_fc24_643f_a768_0d1cd680a825_TB2902_00 FV = 10,000 × (1.0175 11ea7fdb_fc24_6440_a768_0dd2013b517a_TB2902_00 = $14,147.78
Using a financial calculator:
N = 20, I/Y = 1.75, PV = -10,000, PMT = 0, cpt FV = $14,147.78

Question 16

Molly Costner deposits $2,500 in her checking account today.Her checking account pays interest of 2.5% compounded annually.Assuming Molly does not withdraw any funds and does not deposit any additional funds,how much will be in her account in 25 years?
A) $4,096.54
B) $3,750.00
C) $4,102.52
D) $4,634.86
E) $4,062.50

Accepted Answer

FV = PV × 11ea7fdb_fc24_3d2d_a768_dfcabd2be7f1_TB2902_00 FV = 2,500 × (1.025 11ea7fdb_fc24_3d2e_a768_9f2dca87b083_TB2902_00 = $4,634.86
Using a financial calculator:
N = 25, I/Y = 2.5, PV = -2500, PMT = 0, cpt FV = $4,634.86

Question 17

The future value of $100 received today and deposited in an account for four years paying semiannual interest of 6 percent is:
A) $450
B) $126
C) $889
D) $134
E) $124

Accepted Answer

FV = PV × 11ea7fdb_fc23_c7f7_a768_9735b01ca422_TB2902_00 FV = 100 × (1.03 11ea7fdb_fc23_c7f8_a768_1121d4250243_TB2902_00 = $126.68
Using a financial calculator:
N = 8, I/Y = 3, PV = -100, PMT = 0, cpt FV = $126.68

Question 18

At 15% interest compounded annually,approximately how long will it take Walter to double his money?
A) About five years
B) About three years
C) About seven years
D) About fifteen years
E) About fifty years

Accepted Answer

Using a financial calculator:
I/Y = 15, PV = -1, PMT = 0, FV = 2, cpt N = 4.96

Question 19

The future value of a dollar ________ as the interest rate increases and ________ the farther in the future an initial deposit is to be received.
A) decreases; decreases
B) decreases; increases
C) increases; increases
D) increases; decreases

Accepted Answer

Higher interest rates and more compounding periods increase the future value of a dollar.

Question 20

If a United States saving bond can be purchased for $14.60 and has a maturity value at the end of 25 years of $100,what is the annual rate of return on the bond?
A) 6 percent
B) 7 percent
C) 8 percent
D) 9 percent
E) 10 percent

Accepted Answer

i = 11ea7fdb_fc25_eb08_a768_cf48b3d78605_TB2902_00 - 1
i = 11ea7fdb_fc26_1219_a768_8b930507caae_TB2902_00 - 1 = 8%
Using a financial calculator:
N = 25, PV = -14.60, PMT = 0, FV = 100, cpt I/Y = 8%

Quiz 3: Time Value of Money - Introduction

Joe expects to receive a gift of $1,000 when he graduates one year from today.Joe can invest his gift at 6% compounded annually and he would like to use the funds in four years to purchase an engagement ring for Mabel.How much will he have in four years to spend on a ring?

The Vanguard Windsor II mutual fund had a net asset value of $15.07 at the beginning of 1992 and $24.04 at the beginning of 1997.What was the approximate average annual growth rate in this measure over this period? (Round to the nearest whole number)

Casey has $1,000 to invest and would like to buy a $3,000 jet-ski in four years.If interest is compounded annually,what interest rate will she have to receive to reach her goal?

Gary has $1,400 to invest with the goal of having $4,000 available to purchase a used car.If he can earn 12% compounded semiannually on his investment,how long will he have to wait to acquire his car?

When you turned 20,you deposited $1,500 into an account paying interest that is compounded quarterly.You just turned 30,and there is now $2,233.30 in the account.What nominal annual interest rate is the account paying?

If a US Saving bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100,what is the annual rate of return on the bond?

How much will you need in 30 years to have the same purchasing power that $150 has today,if inflation averages 4% per year?

$100 is received at the beginning of year 1,$200 is received at the beginning of year 3.If these cash flows are deposited at 12 percent,their combined future value at the end of year three is: (Round to the nearest whole dollar)

A firm's stock price is $25 per share and is expected to grow at a 5% compound annual rate.What should the stock price per share be in five years?

What is the effective interest rate of 4% compounded quarterly?

If interest rates are 5%,which of the following will produce the largest amount of money in four years?

If $100 is placed in an account that earns a nominal 4%,compounded quarterly,what will it be worth in 5 years?

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is:

Kayla hopes to purchase a new car in five years.If she deposits $10,000 today in an account that pays 7% compounded quarterly,how much will she be able to spend on the new car in five years?

Molly Costner deposits $2,500 in her checking account today.Her checking account pays interest of 2.5% compounded annually.Assuming Molly does not withdraw any funds and does not deposit any additional funds,how much will be in her account in 25 years?

The future value of $100 received today and deposited in an account for four years paying semiannual interest of 6 percent is:

At 15% interest compounded annually,approximately how long will it take Walter to double his money?

The future value of a dollar as the interest rate increases and the farther in the future an initial deposit is to be received.

If a United States saving bond can be purchased for $14.60 and has a maturity value at the end of 25 years of $100,what is the annual rate of return on the bond?