3. Solve the following problems: i.Use equations or the tabular approach to find

Question

3. Solve the following problems:

i.Use equations or the tabular approach to find the following values. You may check your answers using a financial calculator. Disregard rounding differences.

An initial $500 compounded for 1 year at 6%

An initial $500 compounded for 2 years at 6%

The present value of $500 due in 1 year at a discount rate of 6%

The present value of $500 due in 2 years at a discount rate of 6%

ii.Use equations or the tabular approach (and a financial calculator to check your answers) to find the following values.

An initial $500 compounded for 10 years at 6%

An initial $500 compounded for 10 years at 12%

The present value of $500 due in 10 years at a discount rate of 6%

The present value of $500 due in 10 years at a discount rate of 12%

iii.Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1.

$400 per year for 10 years at 10%

$200 per year for 5 years at 5%

$400 per year for 5 years at 0%

Now rework parts a, b, and c assuming that payments are made at the beginning of the year.

iv.Find the present value of the following ordinary annuities.

$400 per year for 10 years at 10%

$200 per year for 5 years at 5%

$400 per year for 5 years at 0%

Now rework parts a, b, and c assuming that payments are made at the beginning of the year.

v.Find the amount to which $500 will grow under each of the following conditions.

12% compounded annually for 5 years

12% compounded semiannually for 5 years

12% compounded quarterly for 5 years

12% compounded monthly for 5 years

vi.Find the present value of $500 due in the future under each of the following conditions.

12% nominal rate, semiannual compounding, discounted back 5 years

12% nominal rate, quarterly compounding, discounted back 5 years

12% nominal rate, monthly compounding, discounted back 1 years

vii.Find the future values of the following ordinary annuities

FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually

FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly

The annuities described in parts a and b have the same total amount of money paid into them during the 5-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns $101.75 more than the one in part a over the 5 years. Why does this occur?

What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity?

ix.Ralph Renner just borrowed $30,000 to pay for a new sports car. He took out a 60-month loan and his car payments are $761.80 per month. What is the effective annual rate (EAR) on Ralph’s loan?

x.Joe Ferro’s uncle is going to give him $250 a month for the next two years starting today. If Joe banks every payment in an account paying 6% compounded monthly, how much will he have at the end of three years?

Explanation / Answer

As per our policy I can not provide answers for so many ques in one go please put these ques separately i) 500x(1.06)^1 530 500x(1.06)^2 561.8 500x1/(1.06)^1 471.6981 500x1/(1.06)^1 444.9982 ii) 500x(1.06)^10 895.4238 500x(1.12)^10 1552.924 500x1/(1.06)^10 279.1974 500x1/(1.12)^10 160.9866 iii) As payments are made at year end for year 1 no interest will be paid or; 1st payment will be compounded for 9 times,2nd for 8 times…last will not compound a year compounding Future value 1 400 (1.10)^9= 2.357948 943.1791 2 400 (1.10)^8= 2.143589 857.4355 3 400 (1.10)^7= 1.948717 779.4868 4 400 (1.10)^6= 1.771561 708.6244 5 400 (1.10)^5= 1.61051 644.204 6 400 (1.10)^4= 1.4641 585.64 7 400 (1.10)^3= 1.331 532.4 8 400 (1.10)^2= 1.21 484 9 400 (1.10)^1= 1.1 440 10 400 (1.10)^0= 1 400 6374.97 b year compounding Future value 1 200 (1.05)^4= 1.215506 243.1013 2 200 (1.05)^3= 1.157625 231.525 3 200 (1.05)^2= 1.1025 220.5 4 200 (1.05)^1= 1.05 210 5 200 (1.05)^0= 1 200 1105.126 c year compounding Future value 1 400 (1.00)^4= 1 400 2 400 (1.00)^3= 1 400 3 400 (1.00)^2= 1 400 4 400 (1.00)^1= 1 400 5 400 (1.00)^0= 1 400 2000 If payments are made at the beginning of the year;year 1 payment is compounded for 10 times…last for 1 time results will be as follows- a year compounding Future value 1 400 (1.10)^10 2.593742 1037.497 2 400 (1.10)^9 2.357948 943.1791 3 400 (1.10)^8 2.143589 857.4355 4 400 (1.10)^7 1.948717 779.4868 5 400 (1.10)^6 1.771561 708.6244 6 400 (1.10)^5 1.61051 644.204 7 400 (1.10)^4 1.4641 585.64 8 400 (1.10)^3 1.331 532.4 9 400 (1.10)^2 1.21 484 10 400 (1.10)^1 1.1 440 7012.467 b year compounding Future value 1 200 (1.05)^5= 1.276282 255.2563 2 200 (1.05)^4= 1.215506 243.1013 3 200 (1.05)^3= 1.157625 231.525 4 200 (1.05)^2= 1.1025 220.5 5 200 (1.05)^1= 1.05 210 1160.383 c year compounding Future value 1 400 (1.00)^5= 1 400 2 400 (1.00)^4= 1 400 3 400 (1.00)^3= 1 400 4 400 (1.00)^2= 1 400 5 400 (1.00)^1= 1 400 2000 Thanks in advance please provide feedback… :-)

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