Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
Prepared by Johnny Howard
© 2015 South-Western, a part of Cengage Learning
23–2 © 2015 South-Western, a part of Cengage Learning
23–3 © 2015 South-Western, a part of Cengage Learning
Annuities
• Annuity
• Present value of an annuity
• Sinking fund
• Future value of an annuity
• Ordinary annuity
• Beginning of the annuity
• End of the annuity
T E R M S
1
23–4 © 2015 South-Western, a part of Cengage Learning
Figure 23.1 Diagram of an Ordinary Annuity
23–5 © 2015 South-Western, a part of Cengage Learning
Figure 23.2 Future Value of an Ordinary Annuity
23–6 © 2015 South-Western, a part of Cengage Learning
to Compute the Future Value of an Annuity
and Total Interest Earned
1. Determine the annuity factor (FVAF) using either a
calculator with exponents or Table 23-1.
2. Multiply the payment amount by the annuity factor
(FVAF). The product is the future value of the
annuity (FVA), including interest.
3. Multiply the payment amount by the number of
payments. The product is the total payments.
4. Subtract the total payments from the future value
of the annuity (FVA). The difference is the total
interest earned.
1
23–7 © 2015 South-Western, a part of Cengage Learning
23–8 © 2015 South-Western, a part of Cengage Learning
to Find the Size of the Payment in an Annuity,
Given Its Future Value
1. Determine the annuity factor (FVAF) using Table
23-1 or a calculator.
2. Divide the future value by the annuity factor. The
quotient is the amount of each payment in the
annuity.
2
23–9 © 2015 South-Western, a part of Cengage Learning
23–10 © 2015 South-Western, a part of Cengage Learning
23–11 © 2015 South-Western, a part of Cengage Learning
Figure 23.3 Present Value of an Ordinary Annuity
23–12 © 2015 South-Western, a part of Cengage Learning
23–13 © 2015 South-Western, a part of Cengage Learning
to Compute the Present Value of an Annuity and
Total Interest Earned
1. Determine the annuity factor (PVAF) using either a
calculator with exponents or Table 23-2.
2. Multiply the payment amount by the annuity factor
(PVAF). The product is the present value of the
annuity (PVA).
3. Multiply the payment amount by the number of
payments. The product is the total of all
payments.
4. Subtract the present value of the annuity from the
total of all payments. The difference is the total
interest earned.
3
23–14 © 2015 South-Western, a part of Cengage Learning
to Find the Size of the Payment in an Annuity,
Given the Present Value
1. Determine the annuity factor (PVAF) using a
calculator or Table 23-2.
2. Divide the present value by the annuity factor
(PVAF). The quotient is the amount of the
payments in the annuity. As a formula, Step 2
could be written as Pmt = PVA ÷ PVAF.
4
23–15 © 2015 South-Western, a part of Cengage Learning
23–16 © 2015 South-Western, a part of Cengage Learning
to Find the Size of the Payment to Amortize a Loan
1. Determine the annuity factor (PVAF) using
Table 23-2 or a calculator.
2. Divide the loan amount by the annuity factor
(PVAF). The quotient is the amount of the
monthly loan payments.
5
23–17 © 2015 South-Western, a part of Cengage Learning
23–18 © 2015 South-Western, a part of Cengage Learning
to Create an Amortization Schedule
For each row except the last:
1. Interest payment = Unpaid balance × Monthly interest rate
2. Principal payment = Monthly payment – Interest payment
3. New unpaid balance = Old unpaid balance – Principal
payment
For the last row:
1. Interest payment = Unpaid balance × Monthly interest rate
2. (Then ADD) Monthly payment = Unpaid balance + Interest
payment
3. Principal payment = Unpaid balance
6
23–19 © 2015 South-Western, a part of Cengage Learning
23–20 © 2015 South-Western, a part of Cengage Learning
Chapter Terms for Review
annuity
future value of an annuity
future value of an annuity factor (FVAF)
ordinary annuity
present value of an annuity
present value of an annuity factor (PVAF)
sinking fund
time line
23–21 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
A For each of the following annuities, find the future value or the amount of the periodic
payment. Round answers to the nearest cent.
23–22 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
A For each of the following annuities, find the future value or the amount of the periodic
payment. Round answers to the nearest cent.
23–23 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
B For each of the following annuities, find the future value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent.
23–24 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
B For each of the following annuities, find the future value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent.
23–25 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
B For each of the following annuities, find the future value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent.
23–26 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
C In each of the following applications, find the future value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–27 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
C In each of the following applications, find the future value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–28 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
C In each of the following applications, find the future value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–29 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
C In each of the following applications, find the future value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–30 © 2015 South-Western, a part of Cengage Learning
Assignment 23.1: Annuities—Future Value
C In each of the following applications, find the future value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–31 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
A For each of the following annuities, find the present value or the amount of the periodic
payment. Round answers to the nearest cent.
23–32 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
A For each of the following annuities, find the present value or the amount of the periodic
payment. Round answers to the nearest cent.
23–33 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
B For each of the following annuities, find the present value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent.
23–34 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
B For each of the following annuities, find the present value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent.
23–35 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
B For each of the following annuities, find the present value, the amount of the periodic
payment, or the total amount of interest paid. Round answers to the nearest cent.
23–36 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
C In each of the following applications, find the present value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–37 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
C In each of the following applications, find the present value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–38 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
C In each of the following applications, find the present value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–39 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
C In each of the following applications, find the present value of the annuity, the amount of
the periodic payment, or the total amount of interest earned. Round answers to the
nearest cent.
23–40 © 2015 South-Western, a part of Cengage Learning
Assignment 23.2: Annuities—Present Value
D Gary Robinson purchased some new equipment and furniture for his office. Instead of
charging it on a credit card, which had an 18% interest rate, Gary negotiated financing
with the office supply dealer. The total purchase amount was $6,450 and it was amortized
over 4 months. The interest rate was 6% per year, or 0.5% per month. The first three
monthly payments were each $1,632.70. Complete the first three lines of the following
amortization schedule. Round answers to the nearest cent.