Use the appropriate formula located on Illustration 10-1 on page 209 to solve the problem. Bob deposits $5000 at the end of each 6 months for 14 years in an account paying 6% interest compounded semiannually A) Find the amount he will have on deposit at maturity. B) How much interest did Bob earn? Hint: Find the total amount that was deposited by multiplying the total number deposits with amount of each deposit and then subtracting this from the future value. Show the use of the appropriate formulas for each part by indicating the evaluation of the formula with information and provide th answers. Be sure to parts using the provided letters and organize your work neatly.

EBK CONTEMPORARY FINANCIAL MANAGEMENT
14th Edition
ISBN:9781337514835
Author:MOYER
Publisher:MOYER
Chapter5: The Time Value Of Money
Section: Chapter Questions
Problem 24P
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llustration 10-1 Compound Interest Formulas
Formula
If periodic payment is made at
the beginning of each period
When to use
Need to know FV; know PV
FV = PV(1 + i)
IA
Not applicable.
PV
Need to know FV; know PMT
Multiply the result by (1 + i).
(1 + i) -
FV = PMT
IB
PMT PMT PMT PMT
РМТ РМТ РМТ РМТ
Need to know PV; know FV
PV =FV
2A
Not applicable.
(1 + i)
FV
Multiply the result by (1 + i).
PMT PMT PMT PMT
Need to know PV; know PMT
PMT PMT PMT PMT
2B
PV = PMT
(1 + i)"
?
Need to know interest rate; know PV
and FV
FV
- 1
i = ?
Not applicable.
i =
FV
PV
Divide the result by (1 + i).
Need to know PMT; know FV
FV(i)
4A
PMT =
FV
(1 + i)" - 1
FV
Divide the result by (1 + i).
Need to know PMT; know PV
PV(i)
4B
PMT
PV
1-
(1 + i)"
PV
Need to know n; know at least two of these
variables: PV, FV, PMT
PV + (1 + i) (PMT)
- In
(PMI)
(1 + i) (PMT) - FV
PV +
- In
PMT -FV
5*
n= ?
n =
In(1 + i)
n =
In(1 + i)
esent value; FV = future value: PMT = periodic payment; i = interest rate per period, expressed in decimal form; n = total number of periods. The
ymbol In stands for natural logarithm.
Dona S is a comprehensive formula that covers quite a few situations. For this formula, use proper sign convention for PV, FV, and PMT. Think of the
PV
Transcribed Image Text:llustration 10-1 Compound Interest Formulas Formula If periodic payment is made at the beginning of each period When to use Need to know FV; know PV FV = PV(1 + i) IA Not applicable. PV Need to know FV; know PMT Multiply the result by (1 + i). (1 + i) - FV = PMT IB PMT PMT PMT PMT РМТ РМТ РМТ РМТ Need to know PV; know FV PV =FV 2A Not applicable. (1 + i) FV Multiply the result by (1 + i). PMT PMT PMT PMT Need to know PV; know PMT PMT PMT PMT PMT 2B PV = PMT (1 + i)" ? Need to know interest rate; know PV and FV FV - 1 i = ? Not applicable. i = FV PV Divide the result by (1 + i). Need to know PMT; know FV FV(i) 4A PMT = FV (1 + i)" - 1 FV Divide the result by (1 + i). Need to know PMT; know PV PV(i) 4B PMT PV 1- (1 + i)" PV Need to know n; know at least two of these variables: PV, FV, PMT PV + (1 + i) (PMT) - In (PMI) (1 + i) (PMT) - FV PV + - In PMT -FV 5* n= ? n = In(1 + i) n = In(1 + i) esent value; FV = future value: PMT = periodic payment; i = interest rate per period, expressed in decimal form; n = total number of periods. The ymbol In stands for natural logarithm. Dona S is a comprehensive formula that covers quite a few situations. For this formula, use proper sign convention for PV, FV, and PMT. Think of the PV
Use the appropriate formula located on Illustration 10-1 on page 209 to solve the problem.
Bob deposits $5000 at the end of each 6 months for 14 years in an account paying 6% interest compounded semiannually
A) Find the amount he will have on deposit at maturity.
B) How much interest did Bob earn? Hint: Find the total amount that was deposited by multiplying the total number deposits with
amount of each deposit and then subtracting this from the future value.
Show the use of the appropriate formulas for each part by indicating the evaluation of the formula with information and provide the
answers. Be sure to parts using the provided letters and organize your work neatly.
Transcribed Image Text:Use the appropriate formula located on Illustration 10-1 on page 209 to solve the problem. Bob deposits $5000 at the end of each 6 months for 14 years in an account paying 6% interest compounded semiannually A) Find the amount he will have on deposit at maturity. B) How much interest did Bob earn? Hint: Find the total amount that was deposited by multiplying the total number deposits with amount of each deposit and then subtracting this from the future value. Show the use of the appropriate formulas for each part by indicating the evaluation of the formula with information and provide the answers. Be sure to parts using the provided letters and organize your work neatly.
Expert Solution
Step 1

Given:

Semi-annual contribution : $5,000

Annual Interest Rate: 6%

Compounding: Semi-Annual

Number of years over which the contributions are made: 14

Required:

  1. The Future Value of the annuity
  2. The total interest earned on the deposit. 
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