Lecture Three

Question 1

future value

Answer 1

amount to which investments will grow after earning interest

Question 2

simple interest

Answer 2

interest earned only on original (principle) investment, no interest earned on prvious interest

Question 3

compound interest

Answer 3

interest earned on the original investment and previous interest earned

Question 4

example of simple interest when 6% on 1,000

Answer 4

anual interest of 60
goes up 60 every year

Question 5

example of simple interest when 6% on 1,000

Answer 5

would go up 6% depending on the last amount

Question 6

what is the CAGR

Answer 6

compound annual growth rate

Question 7

what is the compound annual growth

Answer 7

Measures the average annual growth rate of an investment over multiple years.

Question 8

compound interest formula

Answer 8

FV =investment x (1+r)^t

Question 9

CAGR formula

Answer 9

(Vn/Vo)^1/t=1+r

Vo= initial Value (starting investment)
Vn = Final Value (after time period)
t = Number of years
r = CAGR (average annual growth rate)

Question 10

example of CAGR when: If an investment grows from $1,000 to $1,338.23 in 5 years, we use

Answer 10

(1,338.23/1000)^1/5-1

CAGR =6%per year, confirming the compound interest effect

Question 11

How Different Interest Rates Affect Growth?

Answer 11

Higher interest rates lead to faster exponential growth
📈 Comparison Over Time:

0% → No growth
5% → Moderate growth
10% → Faster growth
15% → Very fast growth

Question 12

What is (PV)?

Answer 12

Present Value (PV)?

Question 13

definition of PV

Answer 13

The value today of a future amount of money.

Question 14

formula of present value

Answer 14

PV= Future value/(1+r)^t

Question 15

discount rate

Answer 15

Interest rate used to compute the PV of a future
value (or cash flow).

Question 16

discount factor

Answer 16

can be used to determine the PV of a future
value (or cash flow

Question 17

rearrange the CAGR

Answer 17

1+r = (FV/PV)^1/t

Question 18

rearranged CAGR to: Investment grows from £18,000 to £21,000 in 3 year to find r

Answer 18

1+r= (21000/18000)^1/3

1+r=(1.1667)^0.333
(-1)

r=5.3%

Since 5.3% is less than the required 6%, the investment does not meet the required return

Question 19

what does rearranging the PV give us

Answer 19

discount factor

Question 20

formula for the discount factor

Answer 20

1/(1+r)^t

Question 21

rearrange pv to find r

Answer 21

r=(FV/PV)^1/t-1

Question 22

what is a Perpetuities

Answer 22

A perpetuity is a series of equal cash flows that never end.

Question 23

example of a Perpetuities

Answer 23

UK Government Bonds (Consols) that pay perpetual interest

Question 24

Perpetuities formula

Answer 24

PV=C/r

PV = present value
C=periodic cash flow
r=interest rate

Question 25

Perpetuity Example: You invest £1,000,000 at 6% annual return.

Answer 25

C=1,000,000 x 6% You will receive £60,000 per year forever

Question 26

Real-World Perpetuity Examples: Bank Account Paying 10% Interest To withdraw $10,000 per year forever, how much must you invest?

Answer 26

PV=10,000/0.10=100,000 you must invest $100,000 today

Question 27

Real-World Perpetuity Example: You must invest $100,000 today. 🔹 Consol Bond Paying $20 Yearly Coupon Required return 5%

Answer 27

PV= 20/0.05=400 The bond should be worth $400 today.

Question 28

: What is an Annuity

Answer 28

A series of equal cash flows for a fixed period

Question 29

Examples of Annuity

Answer 29

Mortgage payments, bond coupon payments.

Question 30

Formula for Annuity

Answer 30

PV=Cx (1- (1/(1+r^t))/r c =periodic cash flow r = Interest Rate t = Number of years

Question 31

Annuity Example: 💰 You withdraw $2,000 per year for 3 years. ✅ Bank pays 5% interest. What is the present value

Answer 31

Step 1: Discount each cash flow Year 1: $2,000 ÷ (1.05)¹ = $1,904.80 Year 2: $2,000 ÷ (1.05)² = $1,814.00 Year 3: $2,000 ÷ (1.05)³ = $1,727.60 ✅ Total PV = $5,446.40

Question 32

Annuity Factor Shortcut

Answer 32

Instead of discounting each year separately, use an annuity factor! Given annuity factor 2.7232 for 3 years at 5%: PV=2,000×2.7232=5,446.40

Question 33

Annuity factor formula

Answer 33

PV=C X AF PV= present value C= lvl cash flow AF = annutity factor

Question 34

Reverse Annuity Calculation: You invest $37,908 at 10% interest. 🔹 You withdraw the same amount for 5 years. ✅ How much can you withdraw per year?

Answer 34

C=PV/AF 3.7908/37,908 ​ =10,000 You can withdraw $10,000 per year for 5 year

Question 35

Reverse annuity

Answer 35

finds how much you can withdraw per yeaR

Question 36

Example of a discount rate

Answer 36

return required: interest rate