Perpetuity

What is an unsecured loan?

Lending provided to individuals that is not secured on an asset.

Examples. Credit card lending, personal loans, student loans.

It is a risk for a lender.

Why would a bank offer a higher 2 year rate as opposed to a 5 year interest rate. ?

Expectations tell us that interest rates decrease over time, so banks would like to leverage as much as possible on current economic conditions.

Rate of return (ROR) on an investment is the percentage of loss or gain generated by an investment.

Interest rate is indicative of the amount of interest that has to be paid on a loan.

FV = Co x (1 + r)t

PV = Ct x 1/(1+ r)t

PV = annual loan payment x (t year annuity factor)

T year annuity factor = 1/r - 1/r(1+r)t

PV of annuity = C1 x (1/r - 1/r(1+r)t)

Where C1 is the cash flow to be recieved each year.

FV of annuity = PV of annuity x (1+r)t

Annual Percentage rate (APR) - interest rate is annualised using simple interest.

APR = rate per period x periods per year

Effective Annual interest rate (EAR) - interest rate that is annualised using compound interest.

It uses the same logic as rate of return.

Ear = End of year amount - Initial amount / initial amouy

EAR = (1 + rate per period)^periods per year

Perpetuity it is a financial security in which a cash flow is recieved forever, identical cash flow.

Return = Cash flow/Present value

Present value of perpetuity = C1/r

R is the discount rate