Chapter 4, Problem 1Q

a.

Summary Introduction

To Discuss: The definition of PV, I, INT, FV_N, PVA_A, FVA_A, PMT, M and I_NOM.

Explanation of Solution

The definition of PV, I, INT, FV_N, PVA_A, FVA_A, PMT, M and I_NOM is as follows:

• PV: “PV” is denoted as “Present Value”, which is the present worth of a stream of payments or future payments which is discounted at a given interest rate. A present value is likewise the beginning amount that is expected to increase in the future.
• INT: “INT” is denoted as “Interest Rate” or I, which is the dollars of amount which is earned every period. The interest can be compounded on various basis such as, annual, semi-annual, quarterly, monthly, daily etc.
• FV_N: “FV_N” is denoted as “Future Value”, which is the closing amount of an account and where” n” is denoted as the number of compounding periods remaining in the account.
• PVA_A: “PVA_A” is denoted as “Present Value of Annuity”, which is the present value of a future stream of equivalent payments.
• FVA_A: “PVA_A” is denoted as “Future Value of Annuity”, which is the closing value of a stream of equivalent payments, where “n” is the number of compounding periods.
• PMT: “PMT” is denoted as “Payment”, which is equivalent to the dollar amount of an equivalent or consistent cash flow.
• M: “M” is denoted as “Number of Compounding Periods per year”. For example annual payments have 1 compounding periods a year and monthly payments have 12 compounding periods a year.
• I_NOM: “I_NOM” is denoted as “Nominal Rate”, or “Interest Rate”.

b.

Summary Introduction

To Discuss: The definition of opportunity cost rate.

Explanation of Solution

The definition of opportunity cost rate is as follows:

The opportunity cost rate (I) of an investment is the interest rate accessible for the best elective investment of comparative risk. The opportunity cost rate is the rate of interest one could procure on an elective investment with a risk equivalent to the risk of the interest that is being referred to.

c.

Summary Introduction

To Discuss: The definition of annuity, lump-sum payment, cash flows and uneven cash flows.

Explanation of Solution

The definition of annuity, lump-sum payment, cash flows and uneven cash flows is as follows:

• Annuity: An annuity is defined as a series of payments of a fixed amount for a predetermined number of periods.
• Lump-sum payment: A lump-sum payment is defined as a single amount of an annuity, which comprises of one payment happening now or in a future period.
• Cash Flows: A cash flow can be classified into two portions. One is the cash inflow, which is considered as a receipt. The second is the cash outflow, which is considered as the amount paid or a deposit.
• Uneven cash flow stream: It is a series of cash flow wherein the amount changes starting with one period then onto the next. For example: $100 in year and $200 in year 2. 

d.

Summary Introduction

To Discuss: The definition of ordinary annuity and annuity due.

Explanation of Solution

The definition of ordinary annuity and annuity due is as follows:

• Ordinary annuity: It has payments happening during the ending of the period. A deferred annuity is simply one more name for an ordinary annuity.
• Annuity due: It has payments happening toward the start of every period. The payment time frame must be equivalent to the compounding period.

e.

Summary Introduction

To Discuss: The definition of perpetuity.

Explanation of Solution

The definition of perpetuity is as follows:

A perpetuity can be defined as a series of payments of a fixed amount that last forever. In other terms, a perpetuity is an annuity where “n” equivalents infinity.

f.

Summary Introduction

To Discuss: The definition of outflow, inflow, time line and terminal value.

Explanation of Solution

The definition of outflow, inflow, time line and terminal value is as follows:

• Outflow: It is considered as a deposit, amount paid or the cost.
• Inflow: It is considered as a receipt.
• Time line: A time line is a significant device utilized in the analysis of time value of money, it is a graphical portrayal which is utilized to show the timing of each cash flows.
• Terminal value: It is the future value of uneven cash flows.

g.

Summary Introduction

To Discuss: The definition of compounding and discounting.

Explanation of Solution

The definition of compounding and discounting is as follows:

• Compounding: It is the method of determining the future value of a single payment or series of cash payments.
• Discounting: It is the method of determining the present value of a single payment or series of cash payments; it is the reverse of compounding.

h.

Summary Introduction

To Discuss: The definition of annual, semiannual, quarterly, monthly and daily compounding.

Explanation of Solution

The definition of annual, semiannual, quarterly, monthly and daily compounding is as follows:

• Annual compounding: It comprise of interest paid only one time a year.
• Semiannual compounding: It comprise of interest paid twice a year.
• Quarterly compounding: It comprise of interest paid once in 4 months, which makes three payments a year.
• Monthly compounding: It comprise of interest paid 12 times a year.
• Daily compounding: It comprise of interest paid for all the 365 days a year.

i.

Summary Introduction

To Discuss: The definition of effective annual rate, nominal interest rate, APR and periodic rate.

Explanation of Solution

The definition of effective annual rate, nominal interest rate, APR and periodic rate is as follows:

• Effective annual rate: It is the yearly rate under annual compounding, would have delivered a similar future value towards the end of 1 year as was created by progressively visit compounding, for instance quarterly compounding.
• Nominal interest rate: It is the interest rate expressed in an agreement. If the compounding happens every year, the effective annual rate and the interest rate are the equivalent. If the compounding period happens regularly, the effective annual rate is more prominent than the nominal rate.
• APR: It is abbreviated as “Annual Percentage Rate”, which is the nominal interest rate which is compounded annually.
• Periodic rate: It is the rate charged by a financier or paid by a borrower every period. It tends to be a rate for every year, semi-annually, quarterly, monthly and daily or any other time interval.

j.

Summary Introduction

To Discuss: The definition of amortization schedule, principal versus interest component of a payment and amortized loan.

Explanation of Solution

The definition of amortization schedule, principal versus interest component of a payment and amortized loan is as follows:

• Amortization schedule: An amortization schedule is a table that separates the periodic interest payments into its principal and interest payments.
• The principal component of every payment decreases the rest of the principal balance. The interest component is the interest payment on the start of-period balance of principal.
• Amortized loan: It is a type of loan that is reimbursed in equivalent intervallic amounts.