5.3: Compound Interest

Question 2

What is compound interest?

Answer 2

Interest that is earned on the principal amount invested and on any accrued interest.

Question 3

How is compound interest different from simple interest?

Answer 3

Compound interest is earned on both the principal and the interest accrued over time, whereas simple interest is only earned on the principal.

Question 4

What is the formula to calculate the future value (FV) using compound interest?

Answer 4

A: ( FV_n = PV_0 (1 + k)^n )

Question 5

What does FVIF stand for and what does it represent?

Answer 5

Future Value Interest Factor (FVIF); it represents the future value of an investment at a given rate of interest for a stated number of periods.

Question 6

How do you calculate the future value of $1,000 invested at 10% annual compound interest for 50 years (Example 5.4)?

Answer 6

A: ( FV_{50} = $1,000 (1 + 0.1)^{50} = $117,390.85 )

Question 7

What is the main takeaway from Example 5.4 regarding long-term compound interest?

Answer 7

Compound interest over a long period can significantly increase the value of an investment compared to simple interest.

Question 8

What are the drawbacks of using the RRSP Home Buyer’s Plan (HBP) according to Finance in the News 5.1?

Answer 8

A:
1. $25,000 isn’t a lot of money when buying a house.
2. You need to repay that money.
3. Paying back your HBP loan isn’t straightforward.

Question 9

Q: How does the compound return differ from the simple average return?

Answer 9

A: Compound return assumes all future returns are reinvested, whereas the simple average does not.

Question 10

What is a basis point?

Answer 10

A: 1/100 of 1 percent.

Question 11

Why do many Canadians find it difficult to repay their HBP loans?

Answer 11

A: Many are unaware of the rules and may not designate their RRSP contributions as HBP repayments, leading to default.

Question 12

What is the definition of discounting in finance?

Answer 12

Finding the present value of a future value by accounting for the time value of money.

Question 13

In Example 5.5, how much does an investor need to invest today to have $1 million in 40 years at a 10% interest rate?

Answer 13

$22,094.93

Question 14

What is the formula for finding the present value (PV) of a future value (FV)?

Answer 14

PV0 = FVn / (1 + k)^n

Question 15

What does PVIF stand for and what does it represent?

Answer 15

Present Value Interest Factor (PVIF);

it determines the present value of $1 to be received at some time in the future based on a given interest rate and period.

Question 16

What is the relationship between PVIF and FVIF?

Answer 16

They are reciprocals of each other. PVIF = 1 / FVIF

Question 17

What are the keystrokes to calculate the present value for Example 5.5 using a financial calculator?

Answer 17

What are the keystrokes to calculate the present value for Example 5.5 using a financial calculator?
A:
1. Enter 0 and press PMT
2. Enter -1,000,000 and press FV
3. Enter 10 and press I/Y
4. Enter 40 and press N
5. Press CPT and then PV
The answer will be $22,094.93.

Question 18

What is the effect of a higher discount rate on present value?

Answer 18

A higher discount rate results in a lower present value.

Question 19

What impact have abnormally low interest rates had on pension funds in recent years?

Answer 19

Low interest rates have increased the present value of pension liabilities, leading to significant deficits for many defined-benefit pension plans.

Question 20

How do you calculate the present value of $1,000,000 to be received in 40 years at a 10% interest rate?

Answer 20

PV = $1,000,000 / (1.1)^40 = $22,094.93

Question 21

Why is discounting important when comparing future values?

Answer 21

It allows comparisons at the current time by converting future values to their present value, accounting for the time value of money.

Question 22

What is the general formula used to solve for future values (FV) and present values (PV) in finance?

Answer 22

FVn = PV0 (1 + k)^n

Question 23

In the context of finding the rate of return, what are the values for a $20,000 investment that grows to $32,000 in five years?

Answer 23

A: FV = $32,000, PV = $20,000, n = 5

Question 24

How do you solve for the interest rate (k) using a financial calculator for an investment that grows from $20,000 to $32,000 in five years?

Answer 24

A:
1. Enter 0 and press PMT
2. Enter 32,000 and press FV
3. Enter -20,000 and press PV
4. Enter 5 and press N
5. Press CPT and then I/Y
The answer will be 9.856%.

Question 25

What is the manual formula to solve for the rate of return (k) when an investment grows from $20,000 to $32,000 in five years?

Answer 25

A: 1.6 = (1 + k)^5

Question 26

In the context of solving for the time period, what are the values for an investment of $20,000 growing to $32,000 at a 10% interest rate?

Answer 26

A: FV = $32,000, PV = $20,000, k = 10%

Question 27

What is the manual formula for solving for time (n) when an investment of $20,000 grows to $32,000 at a 10% interest rate?

Answer 27

n = ln(FV/PV) / ln(1 + k)

Question 28

How do you solve for the time period (n) using a financial calculator for an investment growing from $20,000 to $32,000 at a 10% interest rate?

Answer 28

A:
1. Enter 0 and press PMT
2. Enter 32,000 and press FV
3. Enter -20,000 and press PV
4. Enter 10 and press I/Y
5. Press CPT and then N
The answer will be 4.93 years.

Question 29

What are the four different types of finance problems that can be solved using the equation FVn = PV0 (1 + k)^n?

Answer 29

A:
1. Future value problems
2. Present value problems
3. IRR problems (rate of return)
4. Period problems (time)

Question 30

Explain how to compute future values and present values using compound interest.

Answer 30

Use the formula

FVn = PV0 (1 + k)^n for future values,

PV0 = FVn / (1 + k)^n for present values,

where k is the interest rate and n is the number of periods.

Question 31

What is the relationship between FVIFs and PVIFs? Why does this make sense?

Answer 31

FVIF and PVIF are reciprocals of each other. This makes sense because FVIF is used to calculate future values and PVIF is used to discount future values to present values.

Question 32

Why does compound interest result in higher future values than simple interest?

Answer 32

Because compound interest is earned on both the principal and the interest accrued over time, leading to exponential growth.