important application of compound ✓ interest involves amortized loans. Some common types of amortized loans are automobile loans, home mortgage loans, and business ayment consists of interest and repayment of principal. This breakdown is often developed in an amortization schedule. Interest is largest in the first period and declines in the first period and it increases thereafter. e life of the loan, while the principal repayment is smallest ✓ Show All Feedback ● uantitative Problem: You need $13,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual paymer ith the first payment to be made one year from today. He requires a 5% annual return. What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent. $ . How much of your first payment will be applied to interest and to principal repayment? Do not round intermediate calculations. Round your answers to the nearest cent. Interest: $ Principal repayment: $

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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An important application of compound ✔ interest involves amortized loans. Some common types of amortized loans are automobile loans, home mortgage loans, and business loans. Each loan
in the first period and declines ✓over
payment consists of interest and repayment of principal. This breakdown is often developed in an amortization schedule. Interest is largest
the life of the loan, while the principal repayment is smallest ✓
in the first period and it increases
thereafter.
► Show All Feedback
Quantitative Problem: You need $13,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 4 years,
with the first payment to be made one year from today. He requires a 5% annual return.
a. What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent.
$
b. How much of your first payment will be applied to interest and to principal repayment? Do not round intermediate calculations. Round your answers to the nearest cent.
Interest: $
Principal repayment: $
X
Transcribed Image Text:An important application of compound ✔ interest involves amortized loans. Some common types of amortized loans are automobile loans, home mortgage loans, and business loans. Each loan in the first period and declines ✓over payment consists of interest and repayment of principal. This breakdown is often developed in an amortization schedule. Interest is largest the life of the loan, while the principal repayment is smallest ✓ in the first period and it increases thereafter. ► Show All Feedback Quantitative Problem: You need $13,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 4 years, with the first payment to be made one year from today. He requires a 5% annual return. a. What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent. $ b. How much of your first payment will be applied to interest and to principal repayment? Do not round intermediate calculations. Round your answers to the nearest cent. Interest: $ Principal repayment: $ X
Many assets provide a series of cash inflows over time; and many obligations require a series of payments. When the payments are equal and are made at fixed intervals, the series is an annuity. There
are three types of annuities: (1) Ordinary (deferred) annuity, (2) Annuity due, and (3) Growing annuity. One can find an annuity's future and present values, the interest rate built into annuity
contracts, and the length of time it takes to reach a financial goal using an annuity. Growing annuities are often used in the area of financial planning. Their analysis is more complex and often easier
solved using a financial spreadsheet, so we will limit our discussion here to the first two types of annuities.
The future value of an ordinary annuity, FVAN, is the total amount one would have at the end of the annuity period if each payment (PMT) were invested at a given interest rate and held to the end of
the annuity period. The equation is:
FVAN= PMT
Each payment of an annuity due is discounted for one less
equation is:
[
Each payment of an annuity due is compounded for one additional period, so the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one
additional period. The equation is:
(1+1) N-1
FVAdue=FVA ordinary (1+1)
The present value of an ordinary annuity, PVAN, is the value today that would be equivalent to the annuity payments (PMT) received at fixed intervals over the annuity period. The equation is:
PVAN= PMT
(1+1)N
I
period, so the present value of an annuity due is equal to the present value of an ordinary annuity multiplied by (1 + I). The
PVA due PVA ordinary (1 + I)
One can solve for payments (PMT), periods (N), and interest rates (I) for annuities. The easiest way to solve for these variables is with a financial calculator or a spreadsheet.
Quantitative Problem 1: You plan to deposit $2,300 per year for 6 years into a money market account with an annual return of 2%. You plan to make your first deposit one year from today.
a. What amount will be in your account at the end of 6 years? Do not round intermediate calculations. Round your answer to the nearest cent.
$
b. Assume that your deposits will begin today. What amount will be in your account after 6 years? Do not round intermediate calculations. Round your answer to the nearest cent.
$
Transcribed Image Text:Many assets provide a series of cash inflows over time; and many obligations require a series of payments. When the payments are equal and are made at fixed intervals, the series is an annuity. There are three types of annuities: (1) Ordinary (deferred) annuity, (2) Annuity due, and (3) Growing annuity. One can find an annuity's future and present values, the interest rate built into annuity contracts, and the length of time it takes to reach a financial goal using an annuity. Growing annuities are often used in the area of financial planning. Their analysis is more complex and often easier solved using a financial spreadsheet, so we will limit our discussion here to the first two types of annuities. The future value of an ordinary annuity, FVAN, is the total amount one would have at the end of the annuity period if each payment (PMT) were invested at a given interest rate and held to the end of the annuity period. The equation is: FVAN= PMT Each payment of an annuity due is discounted for one less equation is: [ Each payment of an annuity due is compounded for one additional period, so the future value of an annuity due is equal to the future value of an ordinary annuity compounded for one additional period. The equation is: (1+1) N-1 FVAdue=FVA ordinary (1+1) The present value of an ordinary annuity, PVAN, is the value today that would be equivalent to the annuity payments (PMT) received at fixed intervals over the annuity period. The equation is: PVAN= PMT (1+1)N I period, so the present value of an annuity due is equal to the present value of an ordinary annuity multiplied by (1 + I). The PVA due PVA ordinary (1 + I) One can solve for payments (PMT), periods (N), and interest rates (I) for annuities. The easiest way to solve for these variables is with a financial calculator or a spreadsheet. Quantitative Problem 1: You plan to deposit $2,300 per year for 6 years into a money market account with an annual return of 2%. You plan to make your first deposit one year from today. a. What amount will be in your account at the end of 6 years? Do not round intermediate calculations. Round your answer to the nearest cent. $ b. Assume that your deposits will begin today. What amount will be in your account after 6 years? Do not round intermediate calculations. Round your answer to the nearest cent. $
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