8/10/2019 ACTSC 221 - Review for Final Exam

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ACTSC 221

Review for F inal Exam

Be aware of simple interest and how it differs from compound interest

Know how to calculate accumulated and discounted value for a single payment using a variety of rates and

compounding periods (including continuous compounding) and how to calculate values when a fractional

period of time is involved, or when interest rates change over time

Know how to set up time diagrams and equations of value to calculate equivalent debt payments, investment

amounts.

Understand other applications of compound interest rate theory (population growth, inflation)

Know what an annuity is and the difference between an ordinary annuity, an annuity due, a deferred annuity and

a forborne annuity; know how to calculate accumulated and discounted values of ordinary simple annuities, as

well as annuities due, deferred annuities and forborne annuities (including how to handle changing rates or

payment amounts); given discounted or accumulated value, know how to calculate required payments or the

term of an annuity (both methods)

Know how to calculate the discounted and accumulated value of an annuity when the payment period and the

interest period are not the same (i.e. must either come up with an equivalent payment for the interest period or

an equivalent rate for the payment period). Be aware that if simple interest is used for payments during an

interest period (e.g. monthly payments; interest rate is compounded semi-annually and they pay simple interest

on payments during the interest period), then must come up with an equivalent payment that matches the length

of the interest period; but usually, the first step is to come up with an equivalent rate.

Be comfortable with the calculations for mortgages, i.e. calculating the monthly payment, calculating the O/S

balance, etc. for different amortization periods, at different times, etc..

Know what a perpetuity is and how to calculate the discounted value or periodic payment of a perpetuity.

Know how to calculate the discounted and accumulated value of an annuity whose payments change either by a

constant percentage (i.e. a geometric series) or by a specific amount (arithmetic series). If needed, you will be

given the formulas for the sum of a geometric series and/or an arithmetic series.

Be comfortable with loans repaid via equal principal and interest payments (referred to as the amortization

method in the text)calculating payment amounts, O/S balances, final payment amounts when payments are

rounded up by a cent, etc. Know how to use both the prospective and retrospective method of calculating O/S

balances and when one method is more accurate than the other.

Be comfortable creating an amortization schedule for debts, bonds, sinking funds, etc.

Be comfortable with loans repaid via a single repayment in combination with a sinking fund, i.e. how to

calculate the cost of the debt, the book value of the debt, how to create a sinking fund schedule, etc.

Be able to compare the cost of loans repaid via blended P + I with the cost of loans repaid using a sinking fund

with repayment via an interest only loan, or even repayment by a single P+I payment at the end of the term.

8/10/2019 ACTSC 221 - Review for Final Exam

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Know how to calculate the purchase price of a bond for given coupon rate, yield rate, redemption value, etc.; be

able to construct a bond schedule and be comfortable with schedules for bonds issued at par, issued at a

discount, and issued at a premium.

Know how to calculate the NPV of a capital project given the cash flows and cost of capital. Know what the

capitalized cost of an asset is and how to calculate it (and why). Know what equivalent annual cost is and why it

is used.

Be able to solve stock market problems as per lectures.

Formulas to memorize:

Compound interest:S = P (1+i)n

P = S (1+i)-n

Simple Annuities:S = R *((1+)1)

A = R *(1(1+))

Perpetuity:A =R

i

Know adjustment required when payments occur at the beginning of the payment period (i.e. *(1+i))

Formulas provided:

Simple interest:I = Prt; S = P * (1+rt)

Sum of geometric series:Sn= t1*1

1or Sn= t1*

1

1

Sum of infinite geometric series where r < 1: S =t

1

Sum of arithmetic series:Sn=

2* (1 + n)

For a loan of A to be repaid with equal payments of R over n periods at a rate of i per period:

Interest payment = Ik= R*(1(1+i)-(n-k+1))

Principal payment = Pk= R * (1+i)-(n-k+1)

Outstanding balance= Bk= R *1(1+)()

Principal payments ratio =

= (1+i)