\begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|l|}{ c. Finding PV } \\ \hline Future value (FV) & $1,000 & & \\ \hline Discount rate (I) & 8% & & \\ \hline Number of years (N) & 4 & Formulas & \\ \hline \multicolumn{2}{|l|}{ Present value (PV) } & \multicolumn{2}{|l|}{ \#N/A } \\ \hline \multicolumn{4}{|c|}{ d. Finding the rate of return provided by the security } \\ \hline Cost of security (PV) & $1,000 & & \\ \hline Future value of security (FV) & $3,000 & & \\ \hline Number of years (N) & 4 & & \\ \hline Rate of return (I) & & \multicolumn{2}{|l|}{ \#N/A } \\ \hline \multicolumn{4}{|c|}{ e. Calculating the number of years required to double the population } \\ \hline Current population in millions (PV) & 34.5 & & \\ \hline Growth rate (I) & 3% & & \\ \hline Doubled population in millions (FV) & & \multicolumn{2}{|l|}{ \#N/A } \\ \hline Number of years required to double (N) & & \multicolumn{2}{|l|}{ \#N/A } \\ \hline \multicolumn{4}{|l|}{ f. Finding the PV and FV of an ordinary annuity } \\ \hline Annuity (PMT) & $1,000 & & \\ \hline Interest rate (I) & 14% & & \\ \hline Number of years (N) & 4 & & \\ \hline Present value of ordinary annuity (PV) & & \multirow{2}{*}{\multicolumn{2}{|c|}{#N/A#N/A}} \\ \hline Future value of ordinary annuity (FV) & & & \\ \hline \multicolumn{4}{|c|}{ g. Recalculating the PV and FV for part f if the annuity is an annuity due } \\ \hline Present value of annuity due (PV) & & \multirow{2}{*}{\multicolumn{2}{|c|}{#N/A#N/A}} \\ \hline Future value of annuity due (FV) & & & \\ \hline \multicolumn{4}{|c|}{ h. Recalculating the PV and the FV for parts a and c if the interest rate is semiannually compounded } \\ \hline Future value (FV) & & \#N/A & \\ \hline Present value (PV) & & \#N/A & \\ \hline i. Finding the annual payments for an ordi & Id an ann & nuity due & \\ \hline Present value (PV) & $1,000 & & \\ \hline Discount rate (I) & 6% & & \\ \hline Number of years (N) & 8 & & \\ \hline Annual payment for ordinary annuity (PMT1) & & \#N/A & \\ \hline Annual payment for annuity due (PMT2) & & \#N/A & \\ \hline \end{tabular} Time value of money a. Finding FV Investment (PV) Interest rate (I) Number of years (N) Future value (FV) $1,000 b. Creating a table with FVs at various interest rates and time periods using Data Table \begin{tabular}{|c|r|r|r|} \hline Year (B6) & \multicolumn{3}{|c|}{ Interest Rate (B5) } \\ \hline 0 & 0% & 6% & 20% \\ \hline 1 & & & \\ \hline 2 & & & \\ \hline 3 & & & \\ \hline 4 & & & \\ \hline 5 & & & \\ \hline \end{tabular} Creating a graph with years on the horizontal axis and FV on the vertical axis j. Finding the PV and the FV of an investment that makes the following end-of-year payments \begin{tabular}{|c|c|} \hline Year & Payment \\ \hline 1 & $100 \\ \hline 2 & $200 \\ \hline 3 & $300 \\ \hline \end{tabular} Interest rate (I) 6% Present value of investment (PV) Future value of investment (FV) \#N/A \#N/A k. Five banks offer the same nominal rate on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. (1) Calculating the effective annual rate for each bank and the future values of the deposit at the end of 1 year and 2 years Nominal rate (INOM) Deposit (PV) Number of days per year $3,000 \begin{tabular}{ll} & 365 \\ \hline \end{tabular} Formulas EAR A B C D E FV after 1 year EAR FV after 2 years FV after 1 year FV after 2 years (2) Calculating the nominal rates that will cause all of the banks to provide the same effective annual rate as Bank A Nominal rate (INOM) B C D E Nominal rate (INOM) (3) Calculating the amount of payment to be made annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E Needed amount (FV) Number of years (N) $3,000 1 A B C D E Payment (PMT) I. Setting up the amortization schedule Original amount of mortgage (PV) Interest rate (I) Term to maturity, years (N) $14,000 6% Annual payment (PMT) Formula \#N/A Payment (PMT)