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Question 1 – Periodically Compounded Investment
Suppose that you have available an account that earns 3.65% nominal interest, compounded weekly.
1.1)What is the periodic interest rate, precise to the nearest hundred‐thousandth of a percent?
=3.65%/52 = 0.07019%
1.2)If you deposit $3000 into this account and leave it alone to accrue interest, what will the account be worth after one week?
=(3000*0.07019%)+3000 =
$3002.11
1.3)If you deposit $3000 into this account and leave it alone to accrue interest, what will the account be worth after one year?
=(3000*
(
1+0.0365/52
)
^52 =
$3111.48
1.4)If you deposit $3000 into this account and leave it alone to accrue interest, what will the account be worth after one decade?
=(3000*
(
1+0.0365/52
)
^
(
52*10
)
) =
$4320.99
1.5)What is the APY of this account?
=(
(
1+0.0365/52
)
^52)1 =
3.716%
1.6)What lump sum should you deposit in this account now if you wish the account to be worth $6000 after five years?
Set up 6 columns: Principal, APR (3.65%), Periodic Rate (0.07019%), Time (5), nper (5*52=260), and FV (=principal*(1+periodic rate)^nper).
Goal seek FV by
changing the principal. =
$4999.43
1.7)If you deposit $60 into this account every week (right after the compounding action), what will the account be worth immediately after the 200th deposit?
Use the “=FV
function” =FV(0.07019%,200,60) = $12,878.30
1.8)What size should an identical weekly deposit into this account be in order for the account to be worth $250,000.00 immediately after the 780th deposit?
Set up the
amortization table (7 rows, see paper) =
$240.85
Question 2 Continuously Compounded Investment
Suppose that you have available an account that earns 3.65% nominal interest, compounded continuously.
2.1) If you deposit $3000 into this account and leave it alone to accrue interest, what will the account be worth after one year?
=3000*EXP(3.65%) = $3111.52
2.2) What is the APY of this account?
=(
(
1+0.0365/365
)
^
(
365
)
)1 =
3.717%
Question 3 – Periodically Compounded Loans
You acquire a loan to help you buy a house. The loan is a 25‐year fixed‐rate mortgage with a nominal interest rate of 5.1%, compounded monthly, with identical monthly
payments (made at month end). The amount borrowed is $345,000.
3.1) What will the size of each monthly payment be?
$2036.99
3.2) How much does the balance of the loan decrease in the first month (after the finance charge and monthly payment are applied)?
$570.74
3.3) What is the baseline total cost of the loan (that is, the projected cost if there are no larger‐than‐
usual payments made during the life of the loan)?
$611,096.16
3.4) What is the balance of the loan at the start of the 120th month?
$256,844.26
Use amortization table for all the above
Question 4 – Future Values and Lump Sum Equivalency
Scaling based upon an account that earns an annual interest rate of 3.2%, compounded monthly, and considering these assets:
A promissory note worth $4000 in 7 seven years.
A simple bond which pays the holder $40 at the end of each month for 100 months.
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 Spring '11
 Simonson

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