L2 | Calculating Present Values

Question 1

What is APR?

Answer 1

value-equivalent interest rate paid annually at the end of the year only.

Question 2

What is the formula for the stated/quoted interest rate?

Answer 2

per period interest rate x number of period per year

Question 3

What is continuous compounding?

Answer 3

the mathematical limit that compound interest can reach if it’s calculated and reinvested into an account’s balance over a theoretically infinite number of periods.

Question 4

What is the formula justifying continuous compounding?

Answer 4

An investment of £1 at a rate of r per annum compounded m times a year amounts by the end of the year to [1+(r/m)]^m

whenthemapproachesinfinity,interestrategets continuously compounded and [1+(r/m)]m approaches er

Question 5

What are pensions?

Answer 5

deferred salary

Question 6

What do unfunded pension schemes rely on?

Answer 6

Social contract that current workers pay pensions of retired workers, and anticipate similar future arrangement

Question 7

Who pays funds into funded private sector pension schemes?

Answer 7

employers or employees

Question 8

How do private sector pension schemes become funded?

Answer 8

fund accumulates over time

Question 9

What is the formula for future value of a pension fund/value of pension fund at retirement?

Answer 9

s = percentage of earning, X = earnings, g = growth rate of earnings, r = annual rate of return on savings

Question 10

What is the formula to find the annual amount received from the pension?

Answer 10

Assume 20 because retirement age is 60 and life expectancy is 80, so 20 years to use pension

Question 11

What is the final salary formula?

Answer 11

earnings x (1+g)^(yrs_of_work)

Question 12

What is inflation?

Answer 12

Rate at which general level of prices increases

Question 13

What is the nominal interest rate?

Answer 13

Rate at which the value of investment grows in money terms

Question 14

What is the Real Interest Rate?

Answer 14

Rate at which the purchasing power of an investment increases

Question 15

Fisher Equation

What is the Real Interest Rate formula?

Answer 15

Question 16

What is the formula to approximate the real interest rate?

Answer 16

Question 17

What are the factors of RPI?

Answer 17

• Price of basket of goods: food, clothes, petrol
• Includes housing costs (mortgage payments, rents & council tax)
• Basket is arithmetric average of prices

Question 18

What are the factors of CPI?

Answer 18

• Price of (different) basket of goods
• Excludes housing costs
• Basket is geometric average

Question 19

How should an amortization schedule for a mortgage be set up?

What columns are needed?

Answer 19

1. Month
2. Beginning of month mortgage balance
3. Mortgage repayment
4. Interest
5. Scheduled principal repayment
6. End of month mortgage balance

Question 20

How is mortgage repayment calculated?

Answer 20

Inverting the annuity formula

AV = future value, r = rate, replace pension with monthly repayment, replace 20 with number of monthly payments

Question 21

How is interest calculated?

Answer 21

Beginning of month mortgage balance x monthly IR

Question 22

How is scheduled principle repayment repayment calculated?

Answer 22

mortgage repayment - interest

Question 23

How is the end of month mortgage balance calculated?

Answer 23

Beginning of month mortgage balance - scheduled principal repayment

Question 24

How can a DB (defined benefit) pension’s monthly pension amount be calculated?

Answer 24

Replace 72.1 with correct accrual rate

Question 25

For DC (defined contribution) pensions, what are pensions (liabilities) dependent on?

Answer 25

accumulated value of fund (asset)

Assets = Liabilties

Question 26

What is meant by DB (defined benefit) pensions?

Answer 26

The employer has promused a pension, and must set aside assets to honour this liability

Market Value of Assets = PV (Pension Liability)