Deck 11: Compound Interest and Present Value

Question 1

Using Table 11-1, calculate the compound amount and compound interest for the following investments.

Answer 1

Given,
The principal amount is $42,000,
Time period (years) is 19,
Nominal rate (%) is 11 and
Interest compounded annually.
To calculate compound interest, first find the interest rate per period and the number of compounding periods.
Interest rate per period
Compounding periods = years × Periods per year
Now find the table factor by scanning across the top row of the compound interest table to 11% and down the 11% column to 19 periods.
The table factor at that intersection is 7.26334
The compound amount can be found by multiplying the table factor with the principal.
Compound amount = Table factor × Principal
The amount of interest is found by subtracting the principal form the compound amount
Compound interest = Compound amount - principal
The compound amount and interest for a period of 19 years and at a rate of 11% are $305,060.28 and $263,060.28 respectively.

Question 2

Calculate the present value (principal) and the compound interest for the following investments. Use Table 11-2. Round answers to the nearest cent.

Answer 2

Given,
The compound amount is $5,500,
Term of investment is 15 months,
Nominal rate (%) is 8 and
Interest compounded quarterly.
To solve this present value problem we will use 2% per period (8% nominal rate ÷ 4 period per year) and 5 periods (
year × 4 periods per year)
Step 1 Scan the top row of the present value table to 2%
Step 2 Look down that column to the row corresponding to 5 periods
Step 3 Find the table factor at the intersection of steps 1 and 2 and multiply it by the compound amount to find the present value. Table factor = 0.90573
Present value = table factor × compound amount
The present value is $4,981.515.
Now calculate the compound interest earned by subtracting the present value from the compound amount.
Compound interest = compound amount - present value
Therefore, the compound interest earned is $518.485.

Question 3

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
Over the past 10 years, you've made the following investments:
1. Deposited $10,000 at 8% compounded semiannually in a 3-year certificate of deposit.
2. After the 3 years, you took the maturity value (principal and interest) of that CD and added another $5,000 to buy a 4-year, 6% certificate compounded quarterly.
3. When that certificate matured, you added another $8,000 and bought a 3-year, 7% certificate compounded annually.
a. What was the total worth of your investment when the last certificate matured?
b. What is the total amount of compound interest earned over the 10-year period?

Answer 3

a)
Calculation for 1 st 3 years:
Given,
Deposit $10,000
Nominal rate is 8%
Time period is 3 years and
Interests compound semiannually.
Calculate the compound amount:
Here interest rate per period
Compounding periods = years × Periods per year
The table factor for 6 periods, 4% is 1.26532
Compound amount = Table factor × Principal
Calculation for next 4 years:
Now add $5,000 to the compound amount calculated.
The principal is
Given,
Time period is 4 years,
Interest rate 6% and
Interests compound quarterly.
Calculate the compound amount:
Interest rate per period
Compounding periods = Years × Periods per year
Table factor for 16 periods,
is 1.26899
Compound amount = Table factor × Principal
Calculation for last 3 years:
Now add $ 8,000 to the calculated compound amount.
Principal is
Given,
Time period is 3 years,
Interest rate 7% and
Interests compound annually.
Calculate the compound amount:
Interest rate per periods
Compounding periods = Years × Periods per year
The table factor for 3 periods, 7% is 1.22504
Compound amount = Table factor × Principal
The worth of the investment after 10 years is $37,243.34
(b)
The total amount of compound interest earned over the 10 year period is
Compound interest = Compound amount - Principal
The total amount of compound interest earned over the 10 year period is $14,243.34

Question 4

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 5

Using Table 11-1, calculate the compound amount and compound interest for the following investments.

Question 6

Solve the following word problems by using Table 11-1.
A certain animal husbandry program has a flock of sheep that increases in size by 15% every year. If there are currently 48 sheep, how many sheep are expected to be in the flock in 5 years? Round to the nearest whole sheep.

Question 7

For the following investments, calculate the present value (principal) and the compound interest. Use Table 11-2. Round your answers to the nearest cent.

Question 8

Solve the following exercises and word problems by using the present value formula

Question 9

An amount of money that must be deposited today at compound interest to provide a specified lump sum of money in the future is known as the _______ amount or _______ value.

Question 10

The annual percentage yield (APY) is equal to the total compound interest earned in _______ year divided by the _______.

Question 11

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
Fred North owns Redlands Farms, a successful strawberry farm. The strawberry plants increase at a compound rate of 12% per year. Each year Fred brings new land under cultivation for the new strawberry plants. If the farm has 50 acres of strawberry plants today, how many acres of strawberry plants will the farm have in 8 years? Round to the nearest whole acre.

Question 12

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 13

Using Table 11-1, calculate the compound amount and compound interest for the following investments.

Question 14

Solve the following word problems by using Table 11-1.
The rate of bacteria growth in a laboratory experiment was measured at 16% per hour. If this experiment is repeated and begins with 5 grams of bacteria, how much bacteria should be expected after 12 hours? Round to the nearest tenth of a gram.

Question 15

For the following investments, calculate the present value (principal) and the compound interest. Use Table 11-2. Round your answers to the nearest cent.

Question 16

Solve the following exercises and word problems by using the present value formula

Question 17

The following investments require table factors for periods beyond the table. Create the new table factor and calculate the compound amount for each.

Question 18

The following investments require table factors for periods beyond the table. Create the new table factor and the present value for each.

Question 19

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
At Reliable Trucking, Inc., annual sales are predicted to increase over the next 3 years at a rate of 6% per year. Sales equate to "fleet miles." If Reliable's fleet miles are predicted to reach 4.4 million in 3 years, what is the number of fleet miles today? Round to the nearest tenth of a million.

Question 20

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 21

The following investments require table factors for periods beyond the table. Create the new table factor, rounded to five places, and calculate the compound amount for each.

Question 22

Solve the following exercises and word problems by using the compound interest formula.

Question 23

For the following investments, calculate the present value (principal) and the compound interest. Use Table 11-2. Round your answers to the nearest cent.

Question 24

Solve the following exercises and word problems by using the present value formula

Question 25

The amount of compound interest is calculated by subtracting the _______ from the compound amount.

Question 26

When using the compound interest table or the present value table, the factor is found at the intersection of the rate-per-_______ column and the number-of-_______ row.

Question 27

Solve the following exercises and word problems using formulas.

Question 28

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 29

The following investments require table factors for periods beyond the table. Create the new table factor, rounded to five places, and calculate the compound amount for each.

Question 30

Solve the following exercises and word problems by using the compound interest formula.

Question 31

The following investments require table factors for periods beyond the table. Create the new table factor rounded to five places and calculate the present value for each.

Question 32

Solve the following exercises and word problems by using the present value formula
Alana and Eva Rodriguez are planning a cross-country road trip in 3 years. They estimate $6,000 will be needed to cover expenses. The National Bank of Pinecrest is offering a 3-year CD paying 3.62% interest compounded quarterly.
a. How much should they set aside now to achieve their goal? Round to the nearest whole dollar.
b. How much interest will Alana and Eva earn on the CD?

Question 33

The following investments require table factors for periods beyond the table. Create the new table factor and calculate the compound amount for each.

Question 34

The following investments require table factors for periods beyond the table. Create the new table factor and the present value for each.

Question 35

Solve the following exercises and word problems using formulas.

Question 36

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 37

The following investments require table factors for periods beyond the table. Create the new table factor, rounded to five places, and calculate the compound amount for each.

Question 38

Solve the following exercises and word problems by using the compound interest formula.

Question 39

The following investments require table factors for periods beyond the table. Create the new table factor rounded to five places and calculate the present value for each.

Question 40

Solve the following exercises and word problems by using the present value formula
Mike Gioulis would like to have $25,000 in 4 years to pay offa balloon payment on his business mortgage. His money market account is paying 1.825% compounded daily. Disregarding leap years, how much money must Mike put in his account now to achieve his goal? Round to the nearest whole dollar.

Question 41

Compound interest is actually the _______ interest formula applied a number of times.

Question 42

To use the compound interest formula and the present value formula, you need a calculator with a(n) _______ function ( y x ) key.

Question 43

Solve the following exercises and word problems using formulas.

Question 44

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 45

The following investments require table factors for periods beyond the table. Create the new table factor, rounded to five places, and calculate the compound amount for each.

Question 46

Solve the following exercises and word problems by using the compound interest formula.

Question 47

The following investments require table factors for periods beyond the table. Create the new table factor rounded to five places and calculate the present value for each.

Question 48

You are the finance manager for Olympia Industries. The company plans to purchase $1,000,000 in new assembly line machinery in 5 years.
a. How much must be set aside now at 6% interest compounded semiannually to accumulate the $1,000,000 in 5 years?
b. If the inflation rate on this type of equipment is 4% per year, what will be the cost of the equipment in 5 years, adjusted for inflation?
c. Use the inflation-adjusted cost of the equipment to calculate how much must be set aside now.
d. Use the present value formula to calculate how much would be required now if you found a bank that offered 6% interest compounded daily.

Question 49

For the following investments, compute the amount of compound interest earned in 1 year and the annual percentage yield. Round APY to the nearest hundredth of a percent.

Question 50

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
What is the compound amount and compound interest of $36,000 invested at 12% compounded semiannually for 7 years?

Question 51

Solve the following exercises and word problems using formulas.

Question 52

For the following investments, find the total number of compounding periods and the interest rate per period.

Question 53

The following investments require table factors for periods beyond the table. Create the new table factor, rounded to five places, and calculate the compound amount for each.

Question 54

Solve the following exercises and word problems by using the compound interest formula.
Gabriel Hopen, a 32-year-old commercial artist, has just signed a contract with an advertising agency. Gabriel's starting salary is $47,800. The agency has agreed to increase his salary by 8.5% annually. How much will Gabriel's salary be after 5 years? Round to the nearest whole dollar.

Question 55

The following investments require table factors for periods beyond the table. Create the new table factor rounded to five places and calculate the present value for each.

Question 56

A compound interest table is a useful set of factors that represent the future value of _______ at various interest rates for a number of compounding periods.

Question 57

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
What is the present value of $73,000 in 11 years if the interest rate is 8% compounded semiannually?

Question 58

Solve the following exercises and word problems using formulas.

Question 59

Manually calculate the compound amount and compound interest for the following investments.

Question 60

For the following investments, compute the amount of compound interest earned in 1 year and the annual percentage yield (APY).

Question 61

Solve the following exercises and word problems by using the compound interest formula.
The FernRod Motorcycle Company invested $250,000 at 4.5% compounded monthly to be used for the expansion of their manufacturing facilities. How much money will be available for the project in 3
years?

Question 62

The following investments require table factors for periods beyond the table. Create the new table factor rounded to five places and calculate the present value for each.

Question 63

For the following investments, compute the amount of compound interest earned in 1 year and the annual percentage yield. Round APY to the nearest hundredth of a percent.

Question 64

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
What is the compound amount and compound interest of $15,000 invested at 6% compounded quarterly for 27 months?

Question 65

Solve the following exercises and word problems using formulas.

Question 66

Manually calculate the compound amount and compound interest for the following investments.

Question 67

For the following investments, compute the amount of compound interest earned in 1 year and the annual percentage yield (APY).

Question 68

Solve the following exercises and word problems by using the compound interest formula.
As an incentive to attract savings deposits, most financial institutions today offer daily and even continuous compounding. This means that savings, or passbook, accounts, as well as CDs, earn interest compounded each day or even more frequently, such as every hour or even every minute. (Continuous compounding, in which compounding occurs every instant, involves a different formula that is derived from the formula we've been using.) Let's take a look at daily compounding.
To calculate the compound amount, A , of an investment with daily compounding, use the compound interest formula modified as follows

Question 69

Solve the following word problems by using Table 11-2.
How much must be invested today at 6% compounded quarterly to have $8,000 in 3 years?

Question 70

A shortcut method for calculating approximately how long it takes money to double in value at compound interest is called the Rule of _______.

Question 71

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
What is the annual percentage yield of a $10,000 investment for 1 year at 12% interest compounded monthly?

Question 72

Solve the following exercises and word problems using formulas.

Question 73

Manually calculate the compound amount and compound interest for the following investments.

Question 74

For the following investments, compute the amount of compound interest earned in 1 year and the annual percentage yield (APY).

Question 75

For the following investments, calculate the present value (principal) and the compound interest. Use Table 11-2. Round your answers to the nearest cent.

Question 76

Solve the following word problems by using Table 11-2.
Samantha Wimberly is planning a vacation in Europe in 4 years, after graduation. She estimates that she will need $3,500 for the trip.
a. If her bank is offering 4-year certificates of deposit with 8% interest compounded quarterly, how much must Samantha invest now to have the money for the trip?
b. How much compound interest will be earned on the investment?

Question 77

Using Table 11-1, calculate the compound amount and compound interest for the following investments.

Question 78

Calculate the present value (principal) and the compound interest for the following investments. Use Table 11-2. Round answers to the nearest cent.

Question 79

Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round dollars to the nearest cent and percents to the nearest hundredth of a percent.
City Wide Delivery Service uses vans costing $24,800 each. How much will the company have to invest today to accumulate enough money to buy six new vans at the end of 4 years? City Wide's bank is currently paying 12% interest compounded quarterly.

Question 80

Solve the following exercises and word problems using formulas.