Deck 2: Compound Interest

Question 1

What simple interest rate,r,is equivalent to j₄ = 14% over 18 months?

A)14.48%
B)14.75%
C)15.28%
D)16.74%

Answer 1

15.28%

Question 2

Jim deposits $5000 in an account earning j₁₂ = 9%.He leaves it there for 5 years.How much interest did he earn in the last year (that is,between years 4 and 5)?

A)$671.38
B)$644.13
C)$635.21
D)$565.82

Answer 2

$671.38

Question 3

A long-term promissory note for $40,000 is taken out on June 15,2010.The interest rate on the note is j₄ = 7% and the note is due on December 15,2015.What is the maturity value of the note?

A)$58,589.15
B)$58,398.79
C)$58,597.50
D)$57,581.47

Answer 3

$58,589.15

Question 4

A long-term promissory note for $40,000 is taken out on June 15,2010.The interest rate on the note is j₄ = 7% and the note is due on Dec 15,2015.What is the maturity value of the note?

A)$58,597.50
B)$58,589.15
C)$58,398.79
D)$57,581.47

Question 5

You shop around for the best interest rate and have narrowed your choices to the following:
Bank I: j₁ = 12%
Bank II: j₄ = 11.55%
Bank III: j₁₂ = 11.30%
You wish to have $S in 3 years.What is the present value of S? Put the banks in order,from lowest to highest present value of S.

A)I < II < III
B)III < II < I
C)II < I < III
D)III < I < II

Question 6

What simple interest rate,r,is equivalent to j₁₂ = 9% over a 2-year period?

A)9.82%
B)9.41%
C)9.38%
D)8.30%

Question 7

Rank the following interest rates in the order in which they would give the highest to lowest amount of interest on an investment:
a. j₂ = 15.25%
b. j₄ = 15.1%
c. j₁₂ = 14.85%

A)a > b > c
B)c > a > b
C)c > b > a
D)b > c > a

Question 8

You deposit $10 000 today in a fund that earns interest at j₁ = 4.5%.However,at the end of every year,an expense charge of 0.50% of the accumulated amount of the fund is withdrawn.How much do you have at the end of 3-years?

A)$11,241.34
B)$11,248.64
C)$11,354.60
D)$11,411.66

Question 9

$10,000 was deposited into an investment account earning interest at a nominal rate of 9% compounded monthly for eight years.How much interest was earned in the fifth year?

A)$1468.72
B)$1342.76
C)$1303.11
D)$1270.42

Question 10

Your portfolio of investments consists of a $10,000 loan due at the end of 5 years with interest at j₁ = 10%,and a $25,000 loan due at the end of 10 years with interest at j₁₂ = 6%.What is the present value of this portfolio at j₂ = 8%? (Answer to nearest dollar)

A)$18,165
B)$28,109
C)$31,639
D)$32,029

Question 11

What simple interest rate,r,is equivalent to j₁₂ = 8% over 9 months?

A)8.30%
B)8.22%
C)7.92%
D)4.62%

Question 12

A loan of $15,000 is taken out with interest at j₄ = 8%.What is the total amount of interest due on the loan in the second year?

A)$1338.41
B)$1298.92
C)$1296.00
D)$1200.00

Question 13

What nominal interest rate compounded semi-annually is equivalent to j₅₂ = 13%?

A)12.60%
B)13.41%
C)13.86%
D)14.34%

Question 14

What simple interest rate r is equivalent to j₁₂ = 9% if money is invested for 3.5 years?

A)8.96%
B)9.83%
C)10.53%
D)11.27%

Question 15

What is the total amount of interest earned between the end of 18 months and the end of 36 months on an investment of $1000 if the interest rate is j₁₂ = 9%?

A)$308.65
B)$164.69
C)$154.94
D)$143.96

Question 16

You invest $1500 today and another $2000 18-months from today in a fund earning j₄ = 8% for the first 18 months followed by j₂ = 6% thereafter.How much do you have at the end of 4 years?

A)$4007.79
B)$4274.59
C)$4276.84
D)$4377.73

Question 17

What simple interest rate r is equivalent to j₄ = 8% if money is invested for 4 years?

A)8.24%
B)8.33%
C)9.01%
D)9.32%

Question 18

You are investing a sum of money.Rank the following interest in order of which one will give you the most interest.
a. j₂ = 8.00%
b. j₁₂ = 7.95%
c. j₅₂ = 7.90%

A)c > b > a
B)b > c > a
C)a > b > c
D)b > a > c

Question 19

You invest $5000 into a fund paying interest at j₆ = 9%.How much is in the fund after 3 years?

A)$6350.00
B)$6475.15
C)$6511.30
D)$6536.70

Question 20

What simple interest rate,r,is equivalent to j₆ = 8% over 8 months?

A)16.77%
B)8.16%
C)15.08%
D)7.74%

Question 21

A company has a loan that is due on December 30,2009.At that time they are required to pay $20,000.What was the original amount of the loan if it was taken out on September 30,2007 at j₄ = 12%?

A)$15,290.08
B)$15,328.33
C)$15,498.49
D)$15,516.81

Question 22

A promissory note for $10,000,dated July 1,2007,is due in four years with interest at j₂ = 8%.On October 1,2008,it was sold to an investor who discounted the note at j₄ = 9%.What was the purchase price of the note on October 1,2008?

A)$10,714.46
B)$10,955.53
C)$11,176.77
D)$11,975.31

Question 23

What is the present value of $100,000 due exactly 4 years and 8 months from today if j₂ = 9% and the practical method of discounting is used?

A)$66,324.55
B)$66,310.35
C)$66,296.00
D)$65,358.66

Question 24

You buy a motor boat worth $13,400.You can pay cash,or chose one of two payment options:
Option 1: Pay $10,000 in one year and $5000 in two years
Option 2: Pay $17,400 in 3 years
If the interest rate on both options is j₁₂ = 9%,which one should you take and how much cheaper is it compared to paying cash?

A)Best option is to pay cash
B)1;$17.19
C)1;$78.46
D)2;$103.81

Question 25

Mrs.Singh owes Mr.Valdy $55,513.78 in 14-months.Mr.Valdy agrees to let her repay the loan with a payment of $35,000 in 6-months,$10,000 in 8-months and $X in 14-months.If money is worth j₄ = 6%,what is the value of X,using 14-months as the focal date along with the exact method of crediting/charging interest?

A)$8793.97
B)$9204.40
C)$9230.06
D)$9794.03

Question 26

You invest $50,000 today in a fund earning j₄ = 12%.How much have you accumulated 5 years and 5 months later using the exact method?

A)$93,935.73
B)$93,944.88
C)$94,865.84
D)$94,875.02

Question 27

An individual borrowed $10,000 nine months ago and another $6,000 three months ago and he wishes to pay off this loan with a payment of $X today.You are given that j₂ = 10% and that the practical method of crediting/charging interest is used.Determine $X.

A)$16,918.90
B)$16,912.50
C)$16,907.46
D)$16,900.26

Question 28

You invest $20,000 today in a fund earning interest at j₁ = 4%.How much will you have in 5 years,270 days if the exact method of accumulating is used?

A)$25,063.05
B)$25,059.46
C)$25,053.05
D)$25,049.36

Question 29

You take out a loan of $25,000 from the ABC company.It is due in 5 years with interest at j₂ = 6%.After 18 months,ABC sells your loan to the XYZ company at a price that will earn XYZ a rate of return of j₄ = 5%.What price does XYZ pay?

A)$28,264.75
B)$28,234.61
C)$27,318.18
D)$26,934.58

Question 30

A woman plans to withdraw $1800 18-months from now and $2400 36-months from now.How much does she need to deposit today if the interest rate is j₁₂ = 12% for the first 2 years and j₁₂ = 6% thereafter?

A)$3182.25
B)$3285.18
C)$3510.38
D)$3765.40

Question 31

You invest $50,000 today in a fund earning j₄ = 12%.How much have you accumulated 65 months later using the practical method?

A)$81,038
B)$93,945
C)$94,866
D)$94,875

Question 32

What is the accumulated value of $15,000 over 6 years and 5 months if j₄ = 10% and the exact method of accumulating is used? (Answer to the nearest dollar)

A)$27,411
B)$27,981
C)$28,039
D)$28,271

Question 33

What is the accumulated value of $5000 at the end of 4 years,11 months if j₄ = 9% using the exact method?

A)$7588.52
B)$7638.07
C)$7708.09
D)$7744.89

Question 34

A loan of $A is taken out today.You are given that this loan is to be paid off with a payment of $20,000 in 3 years and 8 months.Determine A,if j₂ = 10% and the practical method of crediting/charging interest is used.

A)$13,988.01
B)$13,984.33
C)$13,980.62
D)$13,762.40

Question 35

The maturity value of a promissory note due on Sept.14,2010 is $6200.What are the proceeds of the note using the practical (approximate)method on Jun.2,2007 if j₂ = 10%?

A)$4454.51
B)$4498.36
C)$4502.80
D)$4760.25

Question 36

Using the exact method,what is the present value of $100,000 due in 19 months if j₄ = 12%? (Answer to nearest dollar. )

A)$82,935
B)$82,927
C)$82,919
D)$82,901

Question 37

A long term promissory note is due on April 5,2013.The maturity value of the note on that date is $4720.56.On June 7,2010,the holder of the notes sells it to a bank who discounts the note at j₂ = 14%.Using the practical method of crediting/charging interest,calculate the proceeds of the sale.

A)$3217.60
B)$3218.30
C)$3219.24
D)$3221.52

Question 38

What is the accumulated value of $5000 for 20 months at j₂ = 11% using the practical method?

A)$5978.85
B)$5976.93
C)$5957.00
D)$5949.88

Question 39

Three payments of $10,000 are made at the end of 3,9 and 15 months respectively.Calculate the total accumulated value of these payments at the end of two years using the exact method with j₆ = 6%.

A)$30,756.65
B)$32,334.08
C)$32,340.10
D)$34,869.82

Question 40

A long term promissory notes for $20 000 is signed on April 15,2010.It is due on October 15,2013 at j₂ = 6%.The maturity value of the note is $24 597.48.The note is sold on April 15,2011 to a bank that discounts the note at j₄ = 8%.What are the proceeds?

A)$21,218.00
B)$20,582.07
C)$20,292.30
D)$20,178.50

Question 41

Using the practical method,what is the accumulated value of $20,000 over 7 years and 10 months if the investment earns interest at j₂ = 10%?

A)$42,898.52
B)$42,953.22
C)$42,964.52
D)$44,350.47

Question 42

A non-interest bearing long term promissory note is due on February 1,2011.The loan amount was $30,000.On October 15^th,2010 the note was sold to a bank that charges interest at j₁₂ = 12%.How much did the bank pay for this note? Assume the exact method is used for fractional time periods.

A)$28,959.25
B)$28,973.20
C)$28,977.85
D)$29,104.21

Question 43

How long will it take for $750 to accumulate to $1000 if j₂ = 9%?

A)6 years,175 days
B)6 years,196 days
C)3 years,88 days
D)3 years,98 days

Question 44

A promissory note with a maturity value of $20,000 is sold to a bank 32-months before maturity.The bank discounts the note using j₂ =16%.What are the proceeds,if the practical method is used?

A)$13,275.57
B)$13,258.11
C)$13,266.92
D)$12,939.48

Question 45

Mrs.Singh owes Mr.Valdy $55 513.78 in 14-months.Mr.Valdy agrees to let her repay the loan with a payment of $35 000 in 6-months,$10 000 in 10-months and $X in 14-months.If money is worth j₄ = 6%,what is the value of X,using 14-months as the focal date along with the exact method of crediting/charging interest?

A)$8894.58
B)$8895.72
C)$8896.37
D)$8897.69

Question 46

You invest $2130.22 today.Four and a half years later,you see that this investment has grown to $3316.08.What nominal rate of interest,j₁₂,have you been earning?

A)9.25%
B)9.88%
C)10.08%
D)10.33%

Question 47

$15,000 is invested into an account that earns interest at j₄ = x%.There are no other deposits made into the account.At the end of 15 years,the accumulated value of the account is $45,000.Determine x.

A)1.85%
B)2.00%
C)7.39%
D)8.00%

Question 48

A non-interest bearing long term promissory note is due on February 1,2011.The loan amount was $30,000.On October 15^th,2010 the note was sold to a bank that charges interest at j₁₂ = 12%.How much did the bank pay for this note? Assume the practical (or approximate)method is used for fractional time periods.

A)$28,962.10
B)$28,952.61
C)$28,829.41
D)$28,675.35

Question 49

A lump sum of $25,000 is due in 4-years and 5 months.What is the present value of this amount using the practical method if the interest rate is j₂ = 8%?

A)$17,681.77
B)$17,679.86
C)$17,677.99
D)$17,685.52

Question 50

What is the present value of $100,000 due in 5-years and 10-months using the practical method if the interest rate is j₄ = 12%?

A)$49,685.31
B)$50,167.50
C)$50,172.39
D)$50,177.24

Question 51

A loan of $A is taken out today.The loan is to be paid off with a payment of $20,000 in 44 months.If the interest rate on the loan is j₂ = 10% and the practical method of crediting/charging interest is used,what is the value of A?

A)$13,988.01
B)$13,762.40
C)$13,984.33
D)$13,980.62

Question 52

You deposit $1000 today in an account that pays interest at j₂ = 8% for the next 5 years and j₂ = 6% thereafter.How many complete interest periods will it take for you to accumulate at least double your original investment?

A)11 periods
B)18 periods
C)21 periods
D)24 periods

Question 53

A $2000 loan is to be repaid with payments of $1200 in 1 year,$800 in 4 years,and $400 in n years,assuming a nominal interest rate of 6% compounded annually.Determine n.

A)4.59
B)6.37
C)9.18
D)14.74

Question 54

An individual borrowed $10 000 nine months ago and another $6000 three months ago and he wishes to pay off this loan with a payment of $X today.You are given that j₂ = 10% and that the practical method of crediting/charging interest is used.Determine $X.

A)$16 918.90
B)$16 912.50
C)$16 907.46
D)$16 900.26

Question 55

You invest $1000 today at j₁₂ = 6%.After 2 years,the interest rate changes to j₁₂ = 12%.How many years from today will it take the $1000 to grow to $10,000?

A)21.28 years
B)20.28 years
C)19.28 years
D)18.28 years

Question 56

An investment doubles in 9 ½ years.What nominal rate of interest j₄ is being earned?

A)7.32%
B)7.36%
C)7.43%
D)7.57%

Question 57

You wish to have $4000 in 3-years time.If you invest $3000 today,what nominal rate j₄ must you earn on your investment to reach your goal?

A)9.62%
B)9.71%
C)10.06%
D)11.11%

Question 58

How long does it take for a loan of $5000 to accumulate $1000 of interest if j₂ = 10%?

A)1 year,10 months,13 days
B)1 year,10 months,29 days
C)3 years,8 months,26 days
D)3 years,9 months,28 days

Question 59

If money triples in 6 years,what rate of interest,j₂,is being earned?

A)9.6%
B)10.0%
C)19.2%
D)20.1%

Question 60

A deposit of $100 is made into an account earning j₁₂ = 18%.Another $100 is deposited into a 2^nd account earning j₂ = 10%.At what time,n (where n is in years),would the accumulated value of the first account be twice as much as the accumulated value in the 2^nd account? (Answer in years)

A)8.5
B)9.3
C)9.9
D)10.2

Question 61

You are given that at a certain rate j₁,money will double itself in 12-years.At this same rate j₁,how many years will it take for $1500 to accumulate $700 of interest?

A)8.2 years
B)6.6 years
C)5.6 years
D)4.2 years

Question 62

If money triples in value in 8 years,what nominal rate of interest compounded semi-annually is being earned?

A)7.11%
B)7.36%
C)14.22%
D)14.72%

Question 63

$25,000 was deposited into an investment account earning interest at a nominal rate of j₂ = x% for 10 years.You are given that the corresponding total amount of interest earned in the first four years is $9,012.22.Determine x.

A)6.25%
B)6.55%
C)7.85%
D)8.00%

Question 64

What is the nominal rate of interest convertible quarterly at which the discounted value (present value)of $15,000 due at the end of 186 months is $5000?

A)9.56%
B)7.39%
C)7.27%
D)7.15%

Question 65

Payments of $1000 due in 6 months,$1500 due in 9 months,and $1200 due in 15 months are to be exchanged for a single payment $X due in 12 months.What is X if j₄ = 6%?

A)$3770.73
B)$3734.99
C)$3809.54
D)$3927.05

Question 66

A car insurance company charges you a premium of $1452 a year for your car insurance policy.You have two options.Option 1 is to pay the $1452 in cash today.Option 2 is to make three payments of $499 at the following times: today,3-months from now and 6-months from now.What nominal rate of interest,j₄,are you being charged?

A)11.73%
B)12.12%
C)12.53%
D)13.06%

Question 67

You deposit $1000 today in an account that pays interest at j₂ = 8% for the next 5-years and j₂ = 6% thereafter.How long in total (in years and days)will it take for you to at least double your original investment?

A)10 years,34 days
B)10 years,67 days
C)10 years,79 days
D)10 years,158 days

Question 68

A debt of $7000 is due with interest at j₂ = 8% at the end of 3 years.To repay this debt,a payment of $1500 is made at the end of 1 year,followed by a payment of $X at the end of 2 years.If money is worth j₄ = 10%,what is the value of X so that the loan is fully paid off?

A)$4685.94
B)$4713.64
C)$5172.40
D)$6873.10

Question 69

Mr.Harry Leggs borrows $5000 today,due with interest at j₄ = 8% in one lump sum at the end of 2 years.Instead,Mr.Leggs wishes to pay $2000 six months from today and $X in 18 months.If money is worth j₁₂ = 6%,what is X?

A)$3252.09
B)$3346.29
C)$3465.95
D)$3562.23

Question 70

Paul deposited $1000 in a savings account paying interest at j₁ = 4.5%.The account has now grown to $1246.18.If he had been able to invest the same amount over twice as long in a fund paying interest at j₁ = 5.5%,to what amount would his investment now have accumulated?

A)$1498.43
B)$1882.35
C)$1653.64
D)$1708.14

Question 71

A loan of $5000 is taken out today.It is due with interest at j₄ = 8% in 2 years.Instead,the borrower negotiates with the lender to pay $2500 in 1 year and $X in 3 years.If the lender can reinvest any payment at j₂ = 5%,what is the value of X?

A)$2493.59
B)$3038.93
C)$3395.34
D)$3581.68

Question 72

A car insurance company charges you a premium of $1452 a year for your car insurance policy.You have two options.Option 1 is to pay the $1452 in cash today.Option 2 is to make two payments of $749 at the following times: today and 6-months from today.What nominal rate of interest,j₄,are you being charged?

A)11.73%
B)13.06%
C)12.88%
D)12.12%

Question 73

You borrows $10,000 today at j₂ = 8%.You pay back $7000 at the end of 2-years and another $7000 at the end of n-years (from today).What is the value of n? (years,days)

A)7 yrs,30 days
B)7 yrs,60 days
C)14 yrs,30 days
D)14 yrs,60 days

Question 74

You borrow $2000 today.The loan is due in 3 years,with interest at j₁ = 9%.It is agreed that you will instead pay $1000 one year from now and $X two years from now.If money is worth j₂ = 6%,what is the value of X?

A)$1190.12
B)$1286.20
C)$1380.48
D)$1529.16

Question 75

A woman borrowed money and owes $3000 one-year from now and $3000 three-years from now.The loan is renegotiated so that the woman can instead pay $X two-years from now and $4000 four-years from now which will fully pay back the loan.If the interest rate on the loan is j₂ = 8%,what is the value of X?

A)$2599.25
B)$2588.42
C)$2580.78
D)$2306.39

Question 76

A student borrows $2,000 today and they agree to pay off the loan with one payment of $2,590.06 to be made at the end of 3 years time.It is then agreed that,instead of paying off the loan with one payment,the student can pay off the loan with a payment of $1000 one year from now and $X two years from now.Given that j₂ = 6%,determine $X.

A)$1190.12
B)$1286.20
C)$1380.48
D)$1529.16

Question 77

$4000 is deposited into an account earning j₂ = 8% for the first 2 years and j₂ = 10% thereafter.How long will it take for it to grow to $9041.67?

A)6 yrs,9 months
B)8 yrs,9 months
C)13 yrs,6 months
D)17 yrs,6 months

Question 78

You borrow $2000 today.This loan is due in 3-years with interest at j₁ = 9%.It is agreed that you will instead pay $1000 one-year from now and $X two-years from now.If money is worth j₂ = 6%,what is the value of X?

A)$1190.12
B)$1286.20
C)$1380.48
D)$1529.16

Question 79

A debt of $5700 is due,with interest at j₂ = 8%,in three years.It is agreed instead that the loan will be repaid with a payment of $X in one year and $3000 in two years.If money is worth j₄ = 4%,what is the value of X?

A)$3282.18
B)$3348.50
C)$3391.45
D)$3777.51

Question 80

If money doubles at a certain rate of interest compounded monthly in 6 years,how long will it take for the same amount of money to triple in value?

A)10.40 years
B)9.51 years
C)8.35 years
D)Cannot be determined