COMPOUND INTEREST and ANNUITIES (review and self-test)

For the tutorial in the box below, first study the problem for a few minutes. Decide how you would translate the words into mathematical language, perhaps writing your thoughts on paper. Then let your mouse wander across the problem, noting how another observer might use and translate the same phrases. Then try the exercises below.


conscience
 
Dear old Harry !

Prof McFarland felt that the student's main difficulty is the "setting up" process, and he hopes that this web device helps the set up in a new and interesting way. Your comments are eagerly invited!

Suggestions for this self exam:
[A] Study your text sections relating to COMPOUND INTEREST and ANNUITIES (Chapter 5 in Rolf), but then keep your book closed during this entire test. For further practice try the interactive tutorial above, or a SELF-GRADING QUIZ
[B] Method choice buttons for each problem show the correct choice when the mouse arrow moves over them. Hence, keep your mouse restrained until you have thought out your response. You may also click on whichever formula (of the 3 shown) is best in solving each problem. Then enter your answer in the box provided, rounding to the nearest dollar.

Recall the meanings of the 8 variables which appear in the 3 formulas used below:
P = "present value" = value of the financial instrument (compound interest or annuity) at its BEGINNING
A = "future value" = value of the financial instrument (compound interest or annuity) at its END or maturity
r = annual rate of interest earned (usually compounded more than once per year).
m = number of times per year interest is compounded, that is, the number of interest periods per year.
i = interest earned during each interest period (again, there are m of these periods per year). Note r = im or i = r/m
n = number of interest periods during the lifetime of the financial instrument (compound interest or annuity)
t = number of years in the lifetime of the financial instrument (compound interest or annuity)
R = (for annuities only) the size of the periodic payment in or out of the annuity
[1] Mr. Smith invested a sum of money five years ago in an account which pays 8% per year compounded quarterly. The account now contains $4OO. What did Mr. Smith invest five years ago?
  Choose
method
first
F
 
Then enter an integer answer to question [1]   F
[2] Find the accumulated amount after 8 years if $12O is invested at an annual rate of 6% compounded semiannually?
  Choose
method
first
F
 
Then enter an integer answer to question [2]   F
[3] A group of investors buys a condominium for $2 million. They pay 1O% down, and agree to pay the rest in 15 equal installments at the end of each year. If interest rates are 8% per year, how much is the first annual payment?
  Choose
method
first
F
 
Then enter an integer answer to question [3]   F
[4] An I.O.U. promises to pay $65O in 5 years. If interest rates are 6% compounded annually, what is this I.O.U. worth today?
  Choose
method
first
F
 
Then enter an integer answer to question [4]   F
[5] A bond promises to pay the owner a sum of $5000 every 3 months for 6O years. If annual interest rates are 8% compounded quarterly, what should be the price of this bond today?
  Choose
method
first
F
 
Then enter an integer answer to question [5]   F
[6] Cathy bought a Mercedes, taking out a loan for $30 000 to help pay for it. She must re-pay the loan in equal monthly payments for 10 years, with an annual interest rate of 6%. What is her monthly payment?
  Choose
method
first
F
 
Then enter an integer answer to question [6]   F
[7] Mr. Jones contributes $5OO into a retirement account at the end of each month for 25 years. If the interest rate remains constant at 6% per year compounded monthly, how much will Mr. Jones have in this account after 25 years?
  Choose
method
first
F
 
Then enter an integer answer to question [7]   F
[8] Paul makes a $2OO down payment on his new PC, and agrees to pay off the rest of the cost at the rate of $1OO per month for 2 years. If the loan company charges an annual interest rate of 12%, what was the ticket price of Paul's PC?
  Choose
method
first
F
 
Then enter an integer answer to question [8]   F
[9] Janice loans Joan a sum of $1OO. Joan is expected to re-pay the loan in one lump sum 3 years from today. If annual interest rates are 6% compounded monthly, what will Joan re-pay to Janice in 3 years?
  Choose
method
first
F
 
Then enter an integer answer to question [9]   F
[10] Mrs. Henderson bought a bond last week for $6970 which promises to pay $1OO every month for 1O years, corresponding to an annual interest rate of 12%. Today, annual interest rates have fallen to 9% for similar bonds, and Mrs. Henderson sells her bond before she receives the first $1OO payment. What price should Mrs. Henderson get for her bond today? Note that even though rates are less today, Mrs. Henderson's bond still promises to pay $100 per month for 10 years.
  Choose
method
first
F
 
Then enter an integer answer to question [10]   F
[11] The Pirerra's are saving up for their trip to Europe. They deposit $150 at the end of each month for 3 years, into an account which earns interest at an annual rate of 9% compounded monthly. How much will this account contain at the end of the 3rd year?
  Choose
method
first
F
 
Then enter an integer answer to question [11]   F