Question

please show your work for 19-21

Problems with a little twist (1-6% unless otherwise stated) 16. If $10000 is deposited today with annual interest rate of 6% and each month is desired to withdraw from this account $100, how many times this monthly withdrawals can be done before the money runs out? 17. If we deposit $100 a month for the next 5 years into an account and at the end of 5 years the account has accumulated $10,000 what is the interest rate earned on this account? 18. Ifwe deposit $100 a month into an account which earns 6% interest annually, for5 consecutive years, how much money exists in this account after ten years? 19. If $100 is deposited into an accountfrom years 1-5. then from years 6-10 nothing is deposited. From years 11-15 again $100 is deposited into that account. How much money is accumulated after the end of 20th year? i-696. 20. If you borrow $10,000 today. Then pay $5000 at the end of 5 years and you decide to pay the rest of that at the end of tenth year, how much do you need to pay? 21. If you deposit $100 a month for ten years and in addition to that you deposit a lump sum of $2000 at the end of 5th year, how much money is accumulated at the end of tenth year? If you stop the deposits at the end of tenth year, how much is accumulated at the end of 15 year? You deposit 200 a month for ten years, a single deposit of 5000 is made at the end of 7th year and another single deposit of 3000 is made at the end of 8th year a. What is the equivalent present worth of this schedule? b. What is the equivalent future worth of this schedule? c. What is the equivalent annual worth of this schedule? 22. 23. You own an air conditioning unit for your house which you have purchased 5 years ago for $5000. You expect the air conditioning unit to work for another 5 years before replacing it, however from years 5 through 10 you are expected to spend an average of $50 a month on the old AC unit. If the new AC unit costs $6000, would it be advisable to change the unit or keep the old one? Hint: Use equivalent present worth 24. To purchase a house you borrow 200K from the bank and decide to pay the loan in 30 years a. What are the monthly payments? b. If you decided to make one extra payment at the end of each year. How many payments do you have to make to repay the loan? MEA72 Page 3

Answer 1

Answer:

Question 16)

Initial Deposited P=$10000

Per months withdraw A=$100

Annual Interest rate =6%

So monthly interest rate =6%/12=0.5%

Let n be number of months before money run out

So 10000=100*(1-(1+0.5%)^-n)/0.5%

(1+0.5%)^-n=0.5

-n*ln(1.005)=ln(0.5)

n=139 months (11 years 7 months)