Deck 9: Compound Interest - Future Value and Present Value

Question 1

Darcy's parents made a trust deposit of $3500.00 on October 31, 2002, to be withdrawn on Darcy's eighteenth birthday on July 31, 2016. To what will the deposit amount on that date at 13.48% compounded quarterly?

Answer 1

PV = 3500.00; i = = 0.0337
October 31, 2002 - July 31, 2016 contains 13 years, 9 months.
n = 13 * 4 + 9/12 * 4 = 52 + 3 = 55
FV = 3500(1 + 0.0337)⁵⁵ = 3500(6.1901104) = 21 665.39

Question 2

Determine the maturity value of $5400 due in 91 months compounding annually at 8.75%.

Answer 2

n = = 7.5833333
FV = 5400.00(1.0875)^7.5833333 = 5400.00(1.8891014) = $10 201.15

Question 3

Calculate the accumulated value of $3000.00 at 8% compounded quarterly for fifteen years. How much of the amount is interest?

Answer 3

PV = 3000; i = = 2% = 0.02 ; n = 15(4) = 60; I/Y = 8; P/Y = C/Y = 4
FV = 3000 = 9843.09
Programmed solution: Interest = 9843.09 - 3000.00 = $6843.09

Question 4

Orange Credit Union expects an average annual growth rate of 16% for the next four years. If the assets of the credit union currently amount to $2.7 million, what will the forecasted assets be in four years?

Question 5

To what future value will a principal of $7100.00 amount in three years at 7.6% p.a. compounded:
a) annually
b) semi-annually
c) quarterly
d) monthly

Question 6

A $8000.00 investment matures in five years, three months. Find the maturity value if interest is 12% p.a. compounded quarterly.

Question 7

A $5725.00 investment matures in three years, seven months. Find the maturity value if interest is 9.16% p.a. compounded quarterly.

Question 8

Determine the accumulated value of $4100.00 compounded semi-annually at 8% p.a. for seven years.

Question 9

Find the future value of and the compound interest on $4575.00 invested at 12.24% compounded monthly for:
a) 3.5 years
b) 7 years
c) 12.5 years

Question 10

Yellowknife Savings offers three-year term deposits at 9.125% compounded annually while your credit union offers such deposits at 8.9% compounded quarterly. If you have $3000 to invest, what is the maturity value of your deposit
a) at Yellowknife Savings?
b) at your credit union?

Question 11

Use the exact method to determine the accumulated value of $3875.00 due in 61 months compounded annually at 9.75% p.a.

Question 12

Find the maturity value of a promissory note for $1400.00 dated March 31, 2001, and due on August 31, 2006, if interest is 7.64% compounded quarterly.

Question 13

How much will a registered retirement savings deposit of $13 500.00 be worth in 11 years at 8.44% compounded quarterly? How much of the amount is interest?

Question 14

Use the exact method to determine the accumulated value of $3875.00 due in 61 months compounded annually at 9.75% p.a.

Question 15

GBC Credit Union expects an average annual growth rate of 10% for the next 10 years. If the assets of the credit union currently amount to $50 million, what will the forecasted assets be in ten years?

Question 16

How much will a registered retirement savings deposit of $10 000.00 be worth in 15 years at 6.00% compounded quarterly? How much of the amount is interest?

Question 17

An investment of $21 700 is accumulated at 5.24% compounded quarterly for three and one-half years. At that time the interest rate is changed to 6.12% compounded monthly. How much is the investment worth two years after the change in interest rate?

Question 18

Find the compound amount of $5700.00 at 11.2% p.a. for seven years compounded monthly.

Question 19

Suppose $4320.00 is invested for five years, eight months at 8.25% compounded annually. What is the compounded amount?

Question 20

Determine the maturity value of $2000 due in 63 months compounding annually at 10%.

Question 21

An investment of $4300.00 earns interest at 9.96% p.a. compounded monthly for four years. At that time the interest rate is changed to 9% compounded semi-annually. How much will the accumulated value be two and a half years after the change?

Question 22

Find the compound interest earned by $500 invested at 3% compounded semi-annually for ten years.

Question 23

Alternative Savings offers five-year term deposits at 10% compounded annually while your credit union offers such deposits at 9.6% compounded quarterly. If you have $1000 to invest, what is the maturity value of your deposit
a) at Alternative Savings?
b) at your credit union?

Question 24

Six years after Ellen deposited $4500 in a savings account that earned interest at 4.68% compounded monthly, the rate of interest was changed to 6.4% compounded semi-annually. How much was in the account thirteen years after the deposit was made?

Question 25

You borrowed $1700.00 at 12.36% p.a. compounded monthly, and repaid $800.00 after three years and $950.00 after five years. How much do you owe at the end of the nine years?

Question 26

Two years after Sean deposited $5000 in a savings account that earned interest at 6% compounded monthly, the rate of interest was changed to 6.4% compounded semi-annually. How much was in the account fifteen years after the deposit was made?

Question 27

Accumulated $1720.00 at 8.4% p.a. compounded monthly from March 1, 2011, to July 1, 2013, and thereafter at 8.88% p.a. compounded quarterly. What is the amount on April 1, 2015?

Question 28

Fahira invested $5000.00 at 4.8% compounded quarterly on January 1, 2012. On July 1, 2013 the rate changed to 5.6% p.a. compounded semi-annually. Calculate the amount Fahira will have on January 1, 2005.

Question 29

A variable rate demand loan showed an initial balance of $20 000.00, payments of $5000.00 after six months, $10000.00 after one year, and a final payment after two years. Interest was 6% compounded semi-annually for the first year and 12% compounded monthly for the remaining time. How much was the size of the final payment?

Question 30

An investment of $5000.00 earns interest at 6% p.a. compounded monthly for two years. At that time the interest rate is changed to 8% compounded semi-annually. How much will the accumulated value be three and a half years after the change?

Question 31

Allison started an RRSP on March 1, 2011, with a deposit of $2470.00. She added $1900.00 on December 1, 2012, and $1850.00 on September 1, 2013. What is the accumulated value of her account on December 1, 2015, if interest is 7.24% compounded quarterly?

Question 32

An investment of $2500.00 accumulates interest at 9.25% compounded quarterly. After 18 months the rate changed to 9.75% compounded semi-annually. Calculate the accumulated value three years after the initial investment.

Question 33

Find the compound interest earned by $1910 invested at 7.5% compounded semi-annually for seven years.

Question 34

The Rob U Blind Bank advertises capital savings at 7.128% compounded semi-annually while Take Your Money Trust offers premium savings at 7.1% compounded monthly. Suppose you have $4400.00 to invest for two years.
a) Which deposit will earn more interest?
b) What is the difference in the amount of interest?

Question 35

Betty deposited $17 150.00 in an RRSP on March 1, 2010, at 6.4% compounded quarterly. Subsequently the interest rate was changed to 6.6% compounded monthly on September 1, 2012, and to 6.8% compounded semi-annually on June 1, 2014. What was the value of the RRSP deposit on December 1, 2016, if no further changes in interest were made?

Question 36

You have a line of credit loan with the Bank of Hong Kong. The initial loan balance was $7000.00. Payments of $3000.00 and $2500.00 were made after four months and ten months respectively. At the end of one year, you borrowed an additional $4250.00. Seven months later, the line of credit loan was converted into a collateral mortgage loan. What was the amount of the mortgage if the line of credit interest was 8.52% compounded monthly?

Question 37

Six years after Mr. Robertson deposited $7110.00 in a savings account that earned interest at 6.8% p.a., compounded semi-annually, the interest was changed to 7.2% p.a., compounded quarterly. How much was in the account ten years after the deposit was made?

Question 38

What is the present value of $7800.00 payable in six years if the current interest rate is 7.6% p.a., compounded quarterly?

Question 39

Sean started an RRSP on March 1, 2007, with a deposit of $2000.00. He added $1500.00 on March 1, 2008. What is the accumulated value of his account on December 1, 2008, if interest is 6% compounded quarterly?

Question 40

The Get What You Pay For Bank advertises capital savings at 12% compounded monthly while Give Me Your Money Trust offers premium savings at 12.36% compounded yearly. Suppose you have $500.00 to invest for two years.
a) Which deposit will earn more interest?
b) What is the difference in the amount of interest?

Question 41

A ten-year promissory note dated April 1, 2001, with a face value of $4700.00 bearing interest at 7.2% compounded semi-annually, discounted seven years later when money was worth 9.92% compounded monthly. Find the proceeds.

Question 42

Find the present value and the compound discount of $6100.00 due in 7.5 years if interest is 8.26% compounded semi-annually.

Question 43

Calculate the present value of $12 500.00 due in two years and nine months if interest is 7.8% p.a. compounded semi-annually.

Question 44

Find the present value and the compound discount of $6 600.00 due in seven years, three months, if interest is 7.2% compounded quarterly.

Question 45

Determine the sum of money that will grow to $18 530 in four years, eleven months at 5.2% compounded quarterly.

Question 46

Find the sum of money that accumulates to $11 415.00 at 7.6% compounded quarterly in six years, seven months.

Question 47

A ten-year promissory note discounted after seven years at 10% compounded quarterly has a maturity value of $40 000. Find the proceeds.

Question 48

Calculate the proceeds of $8956.00 due in seven years, eleven months discounted at 7.5% compounded semi-annually.

Question 49

How much would you have to deposit in an account today to have $37 000.00 in a three-year term deposit at maturity if interest is 7.775% compounded annually?

Question 50

Determine the proceeds of $5000 four years and nine months before the due date if interest is 8% compounded semi-annually.

Question 51

Compute the discounted value of $5125.00 due in three years, eight months if money is worth 8.24% compounded quarterly.

Question 52

A $41 200.00, non-interest-bearing note due August 1, 2003, discounted on March 1, 2001, at 7.32% compounded monthly. Find the proceeds.

Question 53

What sum of money invested at 5.95% p.a., compounded semi-annually, will grow to $28 000.00 in 19.5 years?

Question 54

A seven-year, non-interest-bearing note for $6532.00 is discounted three years and two months before its due date at 9.12% compounded quarterly. Find the proceeds of the note.

Question 55

A $5000.00, six-year note bearing interest at 8.24% compounded quarterly, discounted three and a half years after the date of issue at 6.6% compounded monthly. Find the proceeds.

Question 56

Find the principal which will grow to $7258.00 at 6.58% compounded semi-annually in four years and five months.

Question 57

What sum of money invested at 8% p.a., compounded quarterly, will grow to $10 000.00 in 12.5 years?

Question 58

An eleven-year promissory note discounted after six years at 9.2% compounded quarterly has a maturity value of $71 500. Find the proceeds.

Question 59

What sum of money will grow to $23 000.00 in seven years at 9.612% compounded monthly?

Question 60

Determine the proceeds of $19 000 three years and three months before the due date if interest is 7.6% compounded semi-annually.

Question 61

A debt can be repaid by payments of $1000.00 today, and $3000.00 in two years. What single payment would settle the debt three years from now if money is worth 16% p.a. compounded semi-annually?

Question 62

Loans of $1600.00, $8300.00, and $12 100.00 are due now, in four years, and in seven years respectively. What is the equivalent single sum of money due three and a half years from now if interest is 10.8% compounded monthly?

Question 63

Scheduled debt payments of $1500.00 due seven months ago, $1200.00 due two months ago, and $1800.00 due in five months are to be settled by two equal payments now and three months from now respectively. Determine the size of the equal replacement payments at 9% p.a. compounded monthly.

Question 64

Use the exact method to compute the proceeds of a non-interest-bearing note for $5640.00 six years and seven months before the due date, if money is worth 7.25% p.a. compounded annually.

Question 65

On April 15, 2005, a ten-year note dated June 15, 2001, is discounted at 8.2% compounded quarterly. If the face value of the note is $4000.00 and interest is 7.2% compounded quarterly, find the compound discount.

Question 66

A ten-year note for $2220.00 bearing interest at 6.6% compounded monthly is discounted at 8.92% compounded quarterly four years and four months before maturity. Find the proceeds of the note.

Question 67

Debts of $850 due in six months, $700 due in sixteen months, and $1100 due in three years are to be settled by a single payment one year from now. What is the size of that single payment if interest is 7.5% compounded monthly?

Question 68

A twenty-year note for $10 000.00 bearing interest at 12% compounded monthly is discounted at 8% compounded quarterly four years and six months before maturity. Find the proceeds of the note.

Question 69

A debt payment in the amount of $2000.00 due today, is to be settled by a payment of $1500.00 nine months from now and a final payment in 18 months. Determine the size of the final payment if the money is worth 12% p.a. compounded quarterly. Use the Banker's Method.

Question 70

Four years and five months after its date of issue, a 7-year promissory note for $8900.00 bearing interest at 5.04% compounded monthly is discounted at 6.5% compounded semi-annually. Find the proceeds of the note using the exact method.

Question 71

Two debt payments, the first in the amount of $1600.00 due today, and the second in the amount of $7200.00 due in 15 months with interest at 9.6% p.a. compounded quarterly, are to be settled by a payment of $3400.00 nine months from now and a final payment in 21 months. Determine the size of the final payment if the money is worth 12.12% p.a. compounded monthly.

Question 72

A $4300.00 promissory note issued without interest for nine years on September 30, 2001, is discounted on July 31, 2006, at 8.32% compounded quarterly. Find the compound discount.

Question 73

Debts of $400.00, $450.00 and $500.00 are due in one year, eighteen months and thirty months from now respectively. Determine the single payment now that would settle the debts if interest is 8% p.a. compounded quarterly.

Question 74

An seven-year promissory note for $31 000 dated May 2, 2002, bearing interest at 8% compounded quarterly, is discounted on September 2, 2005, at 8.5% compounded semi-annually. Determine the proceeds of the note.

Question 75

A debt can be repaid by payments of $4125.00 today, $3770.00 in two years and $5600.00 in five years. What single payment would settle the debt three years from now if money is worth 9.88% p.a. compounded quarterly?

Question 76

A note dated May 1, 2011 promises the payment of $5660.00 with interest at 6.5% p.a. compounded semi-annually on November 1, 2015. Find the proceeds of the sale of the note on May 1, 2013 if money was then worth 7.2% p.a. compounded monthly.

Question 77

Determine the discounted value now of $7700.00 due in forty-four months at 7.5% compounded quarterly.

Question 78

Debts of $2800.00 due three months from now and $4600.00 due twenty-one months from now are to be settled by two equal payments due in three months and nine months from now respectively. Determine the size of the equal replacement payments if interest is 5.5% p.a. compounded quarterly.

Question 79

A debt of $5000.00 is to be repaid by payments of $2000.00 after two years, $2500.00 after three years and a final payment after five years. Determine the size of the final payment if interest is 10% p.a. compounded semi-annually.

Question 80

Calculate the proceeds of $5000.00 due in five years, nine months discounted at 8.0% compounded semi-annually.