MATH_2280_Assignment 5
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School
York University *
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Course
2280
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
1
Uploaded by ProfessorHyena2735
M
ATH
2280 M
ATHEMATICAL
T
HEORY
O
F
I
NTEREST
A
SSIGNMENT
5
Due: 11:30pm on Nov. 20, 2023.
1. Donna takes out a loan today and repays the loan with ten level annual payments, with the
first payment one year from today. The payments are calculated based on an annual effective
interest rate of 7.5%. The principal portion of the fifth payment is 471.99.
Calculate the total amount of interest paid on this loan.
2. David buys a new car and finances it with a loan of 20,000. He will make monthly payments
of 420.50 starting in one month with a smaller drop payment (last payment) to pay off the loan.
Payments are calculated using an annual nominal interest rate of 6% convertible monthly.
Immediately after the 15th payment, he repays an additional 1000 and then refinances the loan
to pay off the remaining balance with 24 monthly payments starting one month later. This
refinanced loan uses an annual nominal interest rate of 4.8%, convertible monthly. Calculate
the amount of the new monthly payment. (Hint: It would be better to use the retrospective
approach to find out
OB
15
, as it can avoid the calculation of the final drop payment.)
3. A 10-year annuity-immediate with annual payments of 1000 is selling at 7537.63.
If the
required rate of return for Lucy is 6%, should she invest on this annuity or not?
4. Donde lends 20,000 to Kyle today and charges a nominal interest rate of 7.5% convertible
monthly. Kyle will repay the loan by level payments at the end of each month in the next 5
years. Donde will reinvest the loan payments from Kyle in a fund earning an annual effective
interest rate of 6%.
Determine the annual effective yield for Donde’s investment in the five-year period. (Hint:
Note that all the mortgage payments received are immediately reinvested and the net cash
flows are
0
between time 0 and time 5.)
5. George newly opened an investment account by depositing 2000 on Jan 1. On Mar 1, the
value of the account has increased to 2400 and an additional deposit of 700 is made. On Oct
1, the value has decreased to 2800 and 400 is withdrawn. On the following Jan 1, the account
balance is 2600.
•
Determine the dollar-weighted rate of return for the year.
•
Determine the time-weighted rate of return for the year.
6. A 100 par value 10-year bond sells for
P
and yields a nominal interest rate of
7%
compounded
semiannually. The bond has an annual nominal coupon rate of
6%
and the coupons are payable
semiannually. The redemption value of the bond is 105.
Calculate
P
.
7. A 25-year bond with semiannual coupons, redeemable at par value of 1000, has annual
coupon rate of
7
.
5%
.
Determine the annual effective yield rate if the bond is sold at 950.
1
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