Question

1) How long will it take for $12,000 to become $24,000, if it is in an account paying 3% every six months? 2) A department store charges its customers 1.75% per month for their credit purchases. What nominal interest rate are customers charged? What is the effective rate? 3) You deposit $2,000 in a bank that pays 3% compounded continuously. How much are you going to have at the end of 4 years? 4) A car can be purchased with a $5,000 down payment and 60 monthly payments of $390. If the interest rate is 12%, what is the price of the car? 5) When you retire you want to have enough saved in an account that pays 5% to meet your expenses for the next 20 years. You want to be able to withdraw $50,000 at the end of the first year, and after that, the withdrawals will be reduced by 2,000 per year up to the 20th year. How much should you have in the account when you retire? 6) Helen is evaluating whether a more energy efficient system with a life of 10 years should be installed in an assembly line. Energy savings are estimated to be $500 the 1st year, and increase by 5% annually. If the interest rate is 8%, what is the most that her company can spend to economically justify paying for this system? 7) A bond with a face value of $10,000 and a coupon rate of 5% payable semiannually was bought by an investor today. If the bond matures in 10 years and the investor is satisfied with a 3% return, what was the price of the bond? 8) You buy a new house now and you know that when it becomes 15 years old, you are going to have expenses for repairs that will be about $5,000 a year. You want to deposit now in an account that pays 5% enough to pay for this annual repair need through your life and your children's lives who will inherit the house (i.e., practically forever). How much should be deposited now? 9) Given the following two alternatives, use present worth analysis to find which one should be picked if i=6%. A: First cost = $10,000, Annual benefit = $3,000, Life = 5years B: First cost - $15,000, Annual benefit = $3,000, Life = 10years Numbers 5 and 9 are worth 15 points. All others, 10 points

Answer 1

Solution :- (1)

The Present Value of deposit = $12,000

Future Value = $24,000

Rate of return = 3% for 6 months

Therefore according to equation

$12,000*(1+0.03)ⁿ = $24,000

(1.03)ⁿ = 2

Now with the help of log we find the value of n

n = 23.446

As n is half yearly

n = 23 = 11 years 6 months

And 0.446 = 6*0.446 = 2.67 = 2 months 20 days

Therefore it Means

n = 11 years 8 months 20 days (approx)

As per HomeworkLib policy we need to answer only one question at once so please ask others as seperate one.

If there is any doubt please ask in comments.