1. Formulas

Effective rate (annual rate at which money actually grows during a year)

amount of interest above beginning amount / beginning amount

Future value of an invested amount (FV)

I (capital I) (1 + i)

- I = amount invested at the beginning of the period
- i = interest rate per compounding period
- n = number of compounding periods

Review notes under this formula

Present value (PV)

future value / (1 + i)^n

Review notes under this formula

Formula for PV factor when PV, FV, and n (number of periods) are known

Present value / Future value.

Review notes under this formula

Formula for PV factor when PV, FV, and i (interest rate) is known

Present value / Future value.

Review notes under this formula

Determining Annuity (Payment) Amount When Other Variables are Known

Present value / number from Table 4, "Present value of an ordinary annuity of $1", assuming it is an ordinary annuity where n = # of periods and i = interest

This is when present value, number of periods and interest is known.

Determining number of periods when other variables are known

present value / annuity amount = PVA table factor (Table 4, Present Value of an Ordinary Annuity of $1, assuming it is an ordinary annuity).

Review notes under this formula to finish determining number of periods.

Determining the rate (i) when other variables are known - equal cash flows

present value / annuity amount = PVA factor.

Review notes under this formula to finish determining the rate.

Determining the rate (i) when other variables are known - unequal cash flows

present value = annuity x PVA factor + payment x PV factor

Review notes under this formula to finish determining the interest rate

Review in notes how to determine book value of a bond / price of a bond.

Interest expense for the first six months of a bonds life

carrying value (book value) of the bonds ($169,907,000 for example) x the interest rate (for example can be semiannual effective rate which is half the annual market rate if the bond requires semiannual interest payments)

Amount to pay for each payment for note payments (problem asks what is the amount of annual installment payments for a note)

Amount the note is for / Present value factor

- If a payment is required right away it is an annuity due. - If the first payment is in a year it is an ordinary annuity.