Time Value of Money

A$.$ Ahmad Abu Al$-$Hawa plans to retire $40$ years from now. He expects that he will live $30$ years after his retirement. He wants to have enough money upon reaching retirement age to be able to withdraw $$180,000$ from his account at the end of each year he expects to live. Ahmad plans to accumulate the retirement fund by making an equal deposit at the of each year for the next $40$ years. The interest rate is expected to be $12\%$ in all future periods. How much must Ahmad deposit each year to accumulate the required amount?

B$.$ An investment having a $12\%$ Annual Percentage Rate, has a monthly payment what is the Effective Annual Rate?

C$.$ Amal has faithfully depositing $$2,000$ at the end of each year since the past $5$ years into an account that pays $8\%$ interest semiannually. How much money will she have accumulated in the account

D$.$ Lilian borrows $$50,000$ at $10\%$ annually compounded interest to be repaid in four equal annual installments. What is the actual end$-$of$-$year loan payment? Prepare a loan amortization schedule?

E$.$ Find the present value of the following stream of a firm's cash flows, assuming that the firm's opportunity cost is $10\%.$

$\backslash$table$[[$Year$,$Amount$],[1,$$$5,000$