Please help me with the finance mathematic questions,The question are Finance Math, please calculate and send t me!thanks1. [4 pts] John wishes to accumulate 50,000 with payments of 500 at the end
of each month for as long as needed. Assuming annual interest rate of 8.5% compounded quarterly, find the number of months of regular payments and the amount
remaining after the final regular payment has been made.
2. [4 pts] An annuity pays 600 at the end of each month over a period of four
years. Interest is the first year is a nominal 8% convertible monthly. Interest in
the second year is a nominal 5% convertible monthly. Interest in the third year
is a nominal 7.55% convertible monthly. Interest in the final year is nominal 12%
convertible monthly. Each of these rates applies during its respective year for all
payments. Find the present value of this annuity at inception.
3. [4 pts] A twenty-year annuity-immediate pays 5000 the first year and increases
by X each year thereafter. The interest rate is 6.5% e↵ective annual. If the present
value of this annuity is 70183.23, find the value of X.
4. [4 pts] A perpetuity-immediate has an initial annual payment of 10 and increase
by 5 in each subsequent year. Find the e↵ective annual interest rate at which the
present value of this perpetuity is 2,000.
5. [4 pts] Find the present value and the accumulated value of a continuous annuity
which provides a total monthly payment of 200 for four years. Assume a nominal
annual interest rate of 6% converted monthly.
1. [4 pts] A continuous varying annuity is payable for 20 years, starting at t = 2.
The rate of payment at time t is t2 per annum. Suppose the force of interest at
time t is t = 1/(t + 1) for t 0. Find the present value of the annuity at t = 0.
2. [4 pts] A house is purchased for 350,450. A down payment of 15% is made and
the remainder is financed with a thirty-year fixed loan to be paid o↵ in monthly
installments at the end of each month. Assume the annual interest rate is 9%
a) At what time does the balance reach 50% of the amount originally financed?
b) At what time does the percentage of each payment to principal first exceed 50%?
c) What is the total amount of interest paid?
d) What is the loan balance just after payment number 145?
3. [4 pts] Joe takes out a 7,000 loan which requires sixty equal monthly payments
starting at the end of the first month. The annual interest rate is 8% convertible
monthly. He arranges to make no payments for the first five months and then make
the same payments he would have made plus an extra payment at the end of the
sixtieth month. How much will this balloon payment be?
4. [4 pts] Bob borrows X for ten years at an annual e↵ective interest rate of 8%.
If he pays the principal and interest in one lump sum at the end of ten years he
will pay 468.05 more than if he pays the loan o↵ with level payments at the end
of each year. Find X.
5. [4 pts] A loan is repaid in ten equal annual installments with the first installment
paid one year after the loan is made. The e↵ective annual interest rate is 4%. The
total amount of principal repaid in the fifth, sixth, and seventh payments combined
is 6,083. What is the total amount of interest repaid in the second, third, and
fourth payments combined?
1. [4 pts] Construct the amortization schedule (table) for a five-year annual coupon
bond with face value and redemption value of 20,000. The bond has an annual
coupon rate of 8% and is purchased at a price which yields 4%.
2. [4 pts] A seven-year bond with semiannual coupons and an annual coupon rate
of 8.6% has a face value of 50,000. The bond is redeemable for 45,000 at end of
term and is callable at this same amount in years 4 through 7. Suppose the the
price is 56,973.
(a) What is the maximal annual yield rate convertible semiannually to the investor?
(b) What is the minimal annual yield rate convertible semiannually?
3. [4 pts] A 1000 par value, 10% bond with semiannual coupons is callable 10 years
after issue. The bond matures for 1000 at the end of 20 years, and is sold to yield
a nominal rate of 8% compounded semiannually under the assumption that the
bond will not be called. Calculate the redemption value, at the end of 10 years,
that will yield the same nominal rate of 8% compounded semiannually.
4. [4 pts] Consider two n year 2000 par value bonds. Bond A has 14% semiannual coupons and a price of 2815.4, to yield i, compunded semiannually. Bond B
has 12% semiannual coupons and a price of 2543.6, to yield the same rate i, compounded semiannually. Calculate the price of Bond A to yield i+0.02, compounded
5. [4 pts] A 15-year bond has an annual coupon rate of 8% for the first 5 years, 10%
for the next 5 years, 12% for the last 5 years, and matures at its par value of 1000.
The bond is bought to produce an e↵ective annual yield rate of 10%. Determine
the price of the bond.
1. [4 pts] On January 1, 2019, Bob deposited 90 into an investment account. On
April 1, 2019, when the amount in his account was equal to X, a withdrawal of W
was made. No further deposits or withdrawals were made to his account for the
remainder of the year. On December 31, 2019, the amount in his account was 85.
The dollar-weighted return over the 1-year period was 20%. The time-weighted
return over the 1-year period was 16%.
2. [4 pts] An investment has a value of 100 on January 1, 120 on July 1, and Y on
December 31. There is a deposit Y on July 1 (The deposit is made right after the
investment value is calculated). Over the year, the time-weighted rate of return is
10%. Find the dollar-weighted rate of return.
3. [4 pts] A company owes 10000 to be paid at times 2, 4, and 6. The company
plans to meet the obligation with an investment program that produces asset cash
flows of X at time 1 and Y at time 5. The e↵ective rate of interest is 10%.
(a) Determine X and Y .
(b) Does this investment program satisfy the conditions for immunization?
4. [4 pts] Consider a 15-year mortgage with annual installments. The e↵ective
annual rate of interest is 6%. Compute the Macaulay duration if the mortgage is
prepaid immediately after the third regular payment is made.
5. [4 pts] You are given the following prices of 1000 par value bonds with 10%
annual coupons: The price of a 3-year bond is 1030, the price of a 4-year bond is
1035, and the price of a 5-year bond is 1037. The 3-year spot rate is 8% and the
6-year spot rate is 7%. Find
(a) The 4-year spot rate.
(b) The 5-year spot rate.
(c) Price of a 6-year bond.
6. [4 pts] The term structure is defined by st = 0.05 + 0.005t, for t = 1, 2, 3, 4.
A three-year annuity-immediate will be issued one year from now with annual
payments of 1000. Using the appropriate forward rates, compute the present value
of this annuity one year from now.
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