MATH 106 QUIZ 1 LATEST 2016

| March 14, 2016

Question
1. (24 points) Considering a present value (principal) of $150, and an annual interest rate of 10%,
(a) Showing your work within applicable cells, and providing clarification, if necessary, fill in the cells
with values for each individual year in the following table where the present value is subject to two
different interest-bearing accounts: a simple-interest savings account and a compound-interest savings
account (interest compounded annually).
(b) Having observed the detailed (but simple) computations involved in the table, using appropriate
financial analysis formulas, and showing your formulas and work, determine the interest and future
value for a saving time (term) of three years for
(b1) the simple-interest savings account.
(b2) the compound-interest savings account.
Simple Interest Compound Interest
(Interest Compounded Annually)
Year Annual
Interest
Rate (%)
Present Value
(PV) or
Principal ($)
Interest ($) Future Value (FV)
or Amount ($)
PV Interest ($) Future Value (FV) or
Amount ($)
1
2
3
Total
Interest:
Total
Interest:
Please do not forget Part (b) of the problem, and show work.
2. (7 pts) A credit card balance is one month overdue and subject to an annual interest rate of
29%. If the interest charged for the credit card overdue balance in one month is 632.92, How
much is the overdue balance? Show work.
3. (7 pts) A payday loan is a small, short-term loan to a borrower, offered with the idea that it is
paid back quickly within the next pay period or so. Pay-Later Loans will provide a loan of
$1,500, to be paid back in 45 days with a fee of $240. (The fee is equivalent to an interest
charge). What is the annual rate of interest for this loan? (Assume simple interest with a 360 day
year.) Show work/explanation.
4. (7 pts) Kira arranges for an undisclosed dollar amount of home improvement work to be done
on her house, financed with payments of $816 per month for five and a half years. She paid a
total interest of $3728. Calculate the dollar amount Kira spent on home improvement? Show
work/explanation.
5. (12 pts) (a) Which investment is more advantageous? Show work/explanation.
Option 1: An investment with an annual interest rate of 10.2% and interest compounded semi-annually
or Option 2: An investment with an annual interest rate of 10.1% and interest compounded daily
(b)What is the basis for the comparison called and what does it actually represent? Briefly
explain.
6. (10 pts) A couple has set up a sinking fund in order to have the amount needed in 5 years for
the down payment on a house. The couple paid $3,476.72 quarterly into an account paying 5.8%
annual interest compounded quarterly. How much was the amount the couple needed to collect
via the sinking fund? Show work.
7. (25 pts)
Agatha makes a one-time deposit of $20,000 in a savings account at 3.6% annual interest
compounded monthly.
Bert deposits $600 into a savings account at the end of every month for 5 years at 3.6% annual
interest compounded monthly.
(a) How much will Agatha have in her account at the end of five years? Show work.
(b) How much will Bert have in his account at the end of five years? Show work.
(c) Who has more money, and how much more than the other, in her/his account at the end
of five years, Agatha or Bert? _______ How much more? _________ Show work.
(d) On average, what is the difference between the amounts of two accounts quarterly.
(Equally distribute the total difference over the number of quarters within the time
duration considered.) Show work.
(e) How much has each person earned in total interest, at the end of five years? Show work.
(f) Who earned more in total interest, and how much more than the other, Agatha or Bert?
_________ And how much more? _____________ Show work.
8. (32 pts) To purchase a house, a homebuyer takes out a mortgage, borrowing $285,000 at the
annual interest rate of 4.8%, compounded monthly for 30 years. (The problem has four parts.)
(a) Calculate the monthly payment. Show the formula used and how to carry out the
calculation.
(b) Showing your formula(s) and work below the table, complete the following table. (Round
amounts to the nearest cent.)
Show the calculations necessary to arrive at the entries in the table above.
(c) Calculate the total interest paid if the loan is held for the entire term. Show some work.
(d) (d1) Calculate the unpaid balance after 3 years. Show work.
(d2) What percentage of the amount borrowed is s

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