Problems:

Future and Present Values of Multiple Cash Flows

You deposit $$1,000$ in a savings account that earns $6\%$ annually. Over the next two years, you plan to add $$500$ and $$700$ respectively. Calculate the future value of your account after two years. Assume you make no further deposits after two years and the account continues to earn interest for three more years. What would be the total amount in your account at the end of five years?

Using the above scenario, calculate the present value of these cash flows if the discount rate is $6\%.$

Annuity Calculation

Suppose you win a sweepstakes that offers a $$10$ million prize, paid in equal annual installments over $30$ years. If the discount rate is $5\%,$ what is the present value of this annuity?

You are planning to save for a new car by depositing $$632$ per month for $48$ months into a bank account that offers a monthly interest rate of $1\%.$ How much money can you borrow today based on these deposits?

Perpetuity

A company offers a preferred stock with dividends of $$2\mathrm{.}50$ per quarter indefinitely. If the required return is $10\%$ annually, what is the price of the stock?

Comparing Investment Options

Compare two savings accounts: one offers a $5\mathrm{.}25\%$ interest rate with daily compounding, another offers $5\mathrm{.}3\%$ with semiannual compounding. Calculate the Effective Annual Rate $($EAR$)$ for both and decide which account is more beneficial.

Application of Discounted Cash Flows

Consider an investment that requires a payment of $$100$ today, and in return, you will receive $$40$ in one year and $$75$ in two years. If your required return is $15\%,$ should you accept this investment? Calculate the Net Present Value $($NPV$)$ to make your decision.

Guidelines:

Ensure your answers are well$-$organized and clearly written.

All calculations should be shown step$-$by$-$step.

Include any assumptions you make.