Find the solution using the mathematical equivalence formulae (such as F=P(1+i)n), substitute and solve (with your calculator - not with the tables) for the final answer? Solve by using the proper equivalence expressions (such as F = P(F/P, i, n)) and the tables of equivalence factors. Draw a box around your final answers. APR = Annual Percentage Rate
1. A person wishes to borrow $30,000 from a bank and repay the loan in a single lump sum payment 6 years from the date of the initiation of the loan. If the annual interest rate for the loan is 8%, what is the lump sum payment? (a) Show a cash flow diagram from the standpoint of the borrower. (b) Show a cash flow diagram from the standpoint of the lender. (c, d) Show your calculations and the final answer(s).
2. You are investing in a scheme which will pay you 18% annual interest. You will invest end of period annual amounts of $12,000 until the amount in the account is $240,000. How many years must you invest to reach you goal?
3. You want to by a boat and can afford payments of $350 per month for six years. The monthly interest rate is 0.5%. (a) What is the maximum you can spend on the boat if there is no down payment? (b) What is the maximum you can spend on the boat if you make a down payment of $6000 at the time of purchase?
4. A company needs to buy a building in 4 years, and must fund the down payment from its profits. The purchase will cost $280,000, of which the company can finance $200,000 at 7%. If the company must make the purchase in 4 years and can receive 7% APR on its savings compounded annually, how much must the company save each year to have the required down payment in 4 years?
5. A bank advertises loans with an annual interest rate of 6%. If you borrow $40,000 from the bank and pay it back with equal annual payments over 7 years, (a) what is your annual payment? (b) What is the total interest (in dollars) you have paid to the bank over the life of the loan? Show a cash flow diagram from the standpoint of the borrower. Show your work and final answer(s).
6. You wish to save for a down payment on a car. You can afford to save $400 each month, which you will place into a savings account at the end of each month. The savings account pays you .25% monthly interest. (a) How much have you saved at the end of 4 years? (b) If you need 15% of the purchase price as a down payment, what is the maximum price of the car? Show cash flow diagram from the standpoint of the savings account owner. Show your work and final answer(s).
7. An entrepreneur tells you that if you invest in his company, he will give you the equivalent of 20% APR for five years. (no monthly compounding) At the end of five years, he will pay you back in a lump sum of $80,000. How much do you invest in this opportunity today to achieve the 20% APR? Show a cash flow diagram. Show your work and final answer(s).
8. You invest in a scheme that will pay you $4000 at the end of each of the next six years, plus a lump sum payment of $40,000 when the six years are up. If this scheme boasts a 15% APR, how much must you invest in this opportunity today to achieve the 15% APR?