Question

Please answer the following questions.

1. a) Calculate the present value of $500 with a discount rate of 7% for a period of 10 years. b) Calculate the future value of $1,000 with an interest rate of 5% for a period of 20 years. c) What is the annual interest rate if the present value is S100, future value is $200, and the time period is s years? d) What is the total present value of the following cash flows at an interest rate of 5%? Year 1: $200. Year! 2: 5500; Year 3: 5700 2. a) You believe you will need to have saved 5500,000 by the time you retire in 40 years. If the interest rate is 4% per year, how much must you save each year until retirement to meet your retirement goal? b) A couple thinking about retirement decides to put aside 53.000 each year in a savings plan that earns 8% interest. In 5 years, they will receive a gift of $10,000 that also can be invested. How much money will they have accumulated 30 years from now? c) if the couple in (b) has a poal to retire with $800,000 of savings, how much extra do they need to save every year? 3. A $1.000 General Electric bond pays an annual coupon rate of 8%, has 9 years until maturity, and sells at a yield to maturity of 7%. a) What interest payments will bondholders receive each year? b) At what price does the bond sell if semi-annual interest payments are made? c) What will happen to the bond price if the yield-to-maturity falls to 6% 4. Afirm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of $80.000, with annual maintenance expenses of S10,000. The truck will be sold at the end of 4 years for $20,000. What is the better option if the discount rate is 10%? 5. What will be the monthly payment if you borrow with a $100,000 15-year mortgage at an interest rate of 1% per month? How much of the first payment is interest? How much is principal amortization!

Answer 1

Answer 1)

Present Value = Future Value / ( 1 + Discount rate)^^{number of periods}

Future Value = Initial Investment * ( 1 + Interest rate)^^{number of periods}

Using these:

a) Future Value = $ 500

years = 10 years

Discount rate = 7%

Present Value = 500 / (1 + 7%)^¹⁰

Present Value = 500 / 1.967151357

Present Value = $ 254.1746461

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b)

Initial Investment = $ 1000

Interest Rate = 5%

Years = 20 years

Future Value = 1000 * ( 1 + 5%)^²⁰

Future Value = 1000 * 2.653297705

Future Value = $ 2653.297705

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c)

Initial Investment = $ 100

Future Value = $ 200

Interest Rate = r%

Years = 5 years

200 = 100 * (1 + r%)^⁵

200 / 100 = (1 + r%)^⁵

2 = (1 + r%)^⁵

1.148698355 = 1 + r%

r% = 0.148698355

R = 14.8698355%

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d)

Present Value = Sum of discounted future cash flows

Present Value =  [ 200 / (1 + 5%)^¹ ] + [ 500 / (1 + 5%)^² ] + [ 700 / (1 + 5%)^³ ]

Present Value = 190.48 + 453.51 + 604.69

Present Value = $ 1248.68