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

The present value of $500 due in 1 year at a discount rate of 6%=500/1.06^1=472

The present value of $500 due in 2 years at a discount rate of 6%=500/1.06^2=445

The present value of $500 due in 10 years at a discount rate of 6%=500/1.06^10=279

The present value of $500 due in 10 years at a discount rate of 12%=500/1.12^10=161

$400 per year for 10 years at 10% (FV)=400*(((1+10%)^10-1)/10%)=6374.97 or 6375

$200 per year for 5 years at 5% (FV)=200*(((1+5%)^5-1)/5%)=1105.13 or 1105

$400 per year for 5 years at 0% (FV)=400*5=2000

beginning of the year $400 per year for 10 years at 10% (FV)=(400*(((1+10%)^10-1)/10%))*1.10=7012.47 or 7012

beginning of the year $200 per year for 5 years at 5% (FV)=(200*(((1+5%)^5-1)/5%))*1.05=1160.38 or 1160

beginning of the year $400 per year for 5 years at 0% (FV)=400*5=2000

we do only one question based on chegg rules, I have done three questions as these were short ones.

the above are the answers

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