1.
(Broverman 3rd Ed. Exercise 1.4.8) Smith buys a 182-day US T-bill at a price P182 which
corresponds to a quoted annual discount rate for 182-day T-bills of 8%. 91 days later Smith sells
the T-bill, at a price of P91 at which time the prevailing quoted annual discount rate on 91-day Tbills is also 8%. To the nearest 1/10 percent, find the actual rate of return (91-day interest rate, i
that Smith earned during the time he held the T-bill.
1.7%
1.9%
2.1%
2.3%
The correct answer is not given by (A), (B), (C) or (D)
(4) /4)
(A)
(B)
(C)
(D)
(E)
(C) Solution:
= $95.956
US bills interpret the quoted rate as a discount rate convertible for the period of the bill.
P182 = 100 ×(1 - (182/360) × 0.08)
P91 = 100 × (1 - (91/360) ×0.08) = $97.978
i(4)/4 =P91/ P182 -1 = 97.978/95.956 -1= 2.107% = 2.1%
1.
$1,605
$1,625
$1,645
$1,665
The correct answer is not given by (A), (B), (C) or (D)
(Broverman 3rd Ed. Exercise 1.5.2) Tawny makes a deposit into a bank account which credits
interest at a nominal rate of 8% per annum, convertible semiannually. At the same time, Fabio
deposits 1000 into a different bank account, which is credited with simple interest at rate h. At
the end of five years, the force of interest on the two accounts are equal, and Fabio’s account
has accumulated to Z. Determine Z to the nearest $5.
(A)
(B)
(C)
(D)
(E)
(C) Solution:
Tawny: eδ = (1 + 0.08/2)2
Hence δ = 0.0784414
Hence h = 0.12906
Fabio: A(t) = 1000 ×(1+ ht)
0.0784414 = δ
=(1/A(t)) × dA(t)/dt
= (1/(1+5h) × h
(1+5h)× 0.0784414 = h
Z= 1000 × (1+ 5 ×0.12906) = $1645.30
Less than $305
$305 but less than $315
$315 but less than $325
$325 but less than $335
$335 or more
Susan borrows $30,000 on January 1, 2006 at a rate of 5% per annum
effective, repayable in 60 equal monthly payments, the first being on
February 1, 2006. On August 1, 2008 she makes, in addition to the usual
monthly payment, an extra payment of $9,000 after getting a cash bonus
at work. The bank agrees that the monthly payments beginning with that
on September 1, 2008 should be reduced by an amount R so that the loan
is paid off on the same date as originally agreed. Calculate the reduction
R in the monthly payment.
(A)
(B)
(C)
(D)
(E)
(D): Solution
Can save time by noting that the value of the reduction R equals $9,000
August 1, 2008 payment was the 31st, so there’s 29 left.
9,000 = R a 29⎤ (at 1.051/12 -1 = 0.4074% per month)
= R × 27.3000
Hence R = $329.67