Chapter 5: Time Value of Money – Part 1

This covers Future Value, Present Value, Rate, Number of Periods (NPER). Learn both formulas and Excel methods, and apply to practice problems.

Formulas & Excel Functions

Future Value (FV):
Formula: FV = PV × (1 + r)^n
Excel: =FV(rate, nper, 0, -PV)
Present Value (PV):
Formula: PV = FV ÷ (1 + r)^n
Excel: =PV(rate, nper, 0, -FV)
Interest Rate (RATE):
Formula: r = (FV ÷ PV)^(1 ÷ n) − 1
Excel: =RATE(nper, 0, -PV, FV)
Number of Periods (NPER):
Formula: n = ln(FV ÷ PV) ÷ ln(1 + r)
Excel: =NPER(rate, 0, -PV, FV)

APR vs EAR (quick note)

APR (Annual Percentage Rate) is the nominal rate lenders quote. It ignores intra-year compounding.

EAR (Effective Annual Rate) is the true annual return including compounding. Always: APR ≤ EAR (equal only when compounding once per year).

Convert APR → EAR (m compounding periods/year):
EAR = (1 + APR/m)^m − 1
Excel helper: =EFFECT(APR, m)
Example: =EFFECT(12%, 12) ⇒ 12.68%

Video Explanation

Chapter 5 Questions

Question 1

Suppose you invest $1,000 for 5 years @ 5% interest rate. How much will you have at time 5?

PV = 1,000; r = 5%; n = 5 → FV = 1,000 × (1.05)^5 = $1,276.28
Excel: =FV(5%, 5, 0, -1000)

PV: Rate %: Years (n):

Question 2

Suppose you had a relative deposit $10 at 5.5% 200 years ago. How much will you have today?

PV = 10; r = 5.5%; n = 200 → FV ≈ $447,189.80
Excel: =FV(5.5%, 200, 0, -10)

PV: Rate %: Years (n):

Question 3

Suppose you have $500 to invest and you believe that you can earn 8% per year over the next 15 years. How much would you have at the end of 15 years using compound interest?

PV = 500; r = 8%; n = 15 → FV ≈ $1,586.09
Excel: =FV(8%, 15, 0, -500)

PV: Rate %: Years (n):

Question 4

You want to begin saving for your daughter’s college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?

FV = 150,000; r = 8%; n = 17 → PV ≈ $40,540.34
Excel: =PV(8%, 17, 0, -150000)

FV: Rate %: Years (n):

Question 5

Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much is your initial investment?

FV = 19,671.51; r = 7%; n = 10 → PV = $100,000
Excel: =PV(7%, 10, 0, -19671.51)

FV: Rate %: Years (n):

Chapter 6: Time Value of Money – Part 2

In Chapter 6, we’ll cover PMT, NPV, EAR/APR, annuities, loan amortization, etc. Interactive modules coming soon.

Disclaimer

This tool is for educational use only — for FIN509 simulations or class use. It helps you learn, practice formulas, and use Excel. It is not financial advice.