EXAM FM: FINANCIAL MATHEMATICS

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Format of Exam FM

■ 35 multiple choice questions

■ 3 hours

What Does FM Cover?

Time Value of Money (10-15%)

Annuities (15-20%)

Loans (10-20%)

Bonds (10-20%)

General Cash Flows and Portfolios (15-20%)

Immunization (10-15%)

Interest Rate Swaps (0-10%)

Determinants of Interest Rates (0-10%)

Time Value of Money

■ $1 today isn’t worth the same as a $1 tomorrow!!

■ Potential for the value of money to grow in the future → Earns interest

■ Present Value Function = CF/(1+i)^t

– CF → Cash Flow at time t

– i → Effective Annual Interest Rate

– t → Time

■ Accumulated Value Function = CF(1+i)^t

Example

Suppose Raj has gone broke from betting on the stock market too much. LT has some pity for him, so he decides to give Raj $2,000 four years from now. Assume the interest rate is 5%. What is the present value of LT’s donation?

Another Example!

Solution

Annuities

■ A fixed sum of money paid to someone each year, either for a specific amount of time or forever

■ Think of it this way:

Example

Evelyn owes some student loans to the government. She agrees to pay $10,000 each year for 10 years in the form of an annuity, with the first payment made in one year from now. Assume the interest rate is 5%. What is the present value of Evelyn’s annuity?

Bonds!■ Formal contract to repay borrowed money with interest at fixed time

intervals

■ Some terms to know:– Price → Amount lender pays to the one issuing the bond– Face Value → Value of bond at maturity– Redemption value → Usually same as face value if redeemable at par– Coupon rate → Rate at which fixed payments occur

■ Price of the bond:

Example

Solution

Challenge!

Solution

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