Time value of money

a$.$ Finding FV

Investment $($PV$)$ $$1,000$

Interest rate $($I$)8\%$

Number of years $($N$)6$ Formula

Future value $($FV$)$ #N$/$A

b$.$ Creating a table with FVs at various interest rates and time periods using Data Table Formulas

Year $($B$6)$ Interest Rate $($B$5)$ Year $($B$6)$

$0\%4\%25\%$ #N$/$A

$00$

$11$

$22$

$33$

$44$

$55$

Creating a graph with years on the horizontal axis and FV on the vertical axis

c$.$ Finding PV

Future value $($FV$)$ $$1,000$

Discount rate $($I$)8\%$

Number of years $($N$)6$ Formulas

Present value $($PV$)$ #N$/$A

d$.$ Finding the rate of return provided by the security

Cost of security $($PV$)$ $$1,000$

Future value of security $($FV$)$ $$4,000$

Number of years $($N$)6$

Rate of return $($I$)$ #N$/$A

e$.$ Calculating the number of years required to double the population

Current population in millions $($PV$)35\mathrm{.}8$

Growth rate $($I$)2\%$

Doubled population in millions $($FV$)$ #N$/$A

Number of years required to double $($N$)$ #N$/$A

f$.$ Finding the PV and FV of an ordinary annuity

Annuity $($PMT$)$ $$1,000$

Interest rate $($I$)10\%$

Number of years $($N$)6$

Present value of ordinary annuity $($PV$)$ #N$/$A

Future value of ordinary annuity $($FV$)$ #N$/$A

g$.$ Recalculating the PV and FV for part f if the annuity is an annuity due

Present value of annuity due $($PV$)$ #N$/$A

Future value of annuity due $($FV$)$ #N$/$A

h$.$ Recalculating the PV and the FV for parts a and c if the interest rate is semiannually compounded

Future value $($FV$)$ #N$/$A

Present value $($PV$)$ #N$/$A

i$.$ Finding the annual payments for an ordinary annuity and an annuity due

Present value $($PV$)$ $$1,000$

Discount rate $($I$)7\%$

Number of years $($N$)12$

Annual payment for ordinary annuity $($PMT$1)$ #N$/$A

Annual payment for annuity due $($PMT$2)$ #N$/$A

j$.$ Finding the PV and the FV of an investment that makes the following end$-$of$-$year payments

Year Payment

$1$ $$200$

$2$ $$400$

$3$ $$500$

Interest rate $($I$)7\%$

Present value of investment $($PV$)$ #N$/$A

Future value of investment $($FV$)$ #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$)6\%$

Deposit $($PV$)$ $$4,000$

Number of days per year $365$

Formulas

A B C D E

EAR EAR

FV after $1$ year FV after $1$ year

FV after $2$ years 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

B C D E

Nominal rate $($INOM$)$ 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$)$ $$4,000$

Number of years $($N$)1$

A B C D E

Payment $($PMT$)$ Payment $($PMT$)$

l$.$ Setting up the amortization schedule

Original amount of mortgage $($PV$)$ $$15,000$

Interest rate $($I$)7\%$

Term to maturity, years $($N$)4$

Formula

Annual payment $($PMT$)$ #N$/$A

Formulas

Year Beginning Balance Payment Interest Repayment of Principal Ending Balance Year

$11$

$22$

$33$

$44$

Creating a graph that shows how the payments are divided between interest and principal repayment over time

The data has been collected in the Microsoft Excel file below. Download the spreadsheet and perform the required analysis to answer the questions below. Do not round intermediate calculations. Enter your answers as positive values.

Download spreadsheet Time value of money$-17704$e$.$xlsx

a$.$ Find the FV of $$1,000$ invested to earn $8\%$ after $6$ years. Round your answer to the nearest cent.

$ fill in the blank $2$

b$.$ What is the investment's FV at rates of $0\%,4\%,$ and $25\%$ after $0,1,2,3,4,$ and $5$ years? Round your answers to the nearest cent.

Year Interest Rate

$0\%4\%25\%$

$0$ $ fill in the blank $3$

$1000$

$ fill in the blank $4$

$ fill in the blank $5$

$1$ $ fill in the blank $6$

$1000$

$ fill in the blank $7$

$ fill in the blank $8$

$2$ $ fill in the blank $9$

$1000$

$ fill in the blank $10$

$ fill in the blank $11$

$3$ $ fill in the blank $12$

$1000$

$ fill in the blank $13$

$ fill in the blank $14$

$4$ $ fill in the blank $15$

$1000$

$ fill in the blank $16$

$ fill in the blank $17$

$5$ $ fill in the blank $18$

$1000$

$ fill in the blank $19$

$ fill in the blank $20$