Time value of money (TVM)

What is the core idea of the Time Value of Money (TVM)?

Money today is worth more than the same amount in the future.

Why is money today more valuable than money in the future?

You can invest it to earn returns and it's certain, unlike future money.

What should investment returns compensate for?

Inflation and risk.

What does inflation mean in terms of money's value?

It decreases the purchasing power of money over time.

What does investment risk refer to?

Uncertainty about future cash flows (CFs).

How do investors respond to higher risk?

They demand higher returns to compensate for the increased risk.

What financial decisions use TVM?

Bond and stock valuation, business project decisions, and financial analysis.

What must be done to compare or combine money from different times?

Adjust for time value by calculating the present value of future amounts.

What is Future Value (FV)?

The amount an investment grows to after earning interest over time.

What is the formula for FV with simple interest?

FV = PV × (1 + r × n)

What is the formula for FV with compound interest?

FV = PV × (1 + r)^n

What is the key difference between simple and compound interest?

Simple interest is only on the original principal; compound interest includes interest on previous interest.

Why is compound interest powerful in finance?

Over time, it leads to exponential growth of your investment.

When is simple interest typically used?

For short-term loans, coupon payments, or some savings accounts.

In the compound interest formula FV = PV × (1 + r)ⁿ, what does (1 + r)ⁿ represent?

It is the Future Value Interest Factor (FVIF).

What are two ways to increase FV?

Increasing the number of years for which money is invested, investing at a higher interest rate

What is Present Value (PV)?

The value today of a future cash flow.

What is PVIF (Present Value Interest Factor)?

PVIF = 1 / (1 + r)^n

What causes PV to decrease?

A longer time period or a higher interest rate.

What is the discount rate?

The interest rate used to compute the present value of future cash flows.

What does "compounding periods per year" mean in time value of money (TVM)?

It refers to how often interest is applied (annually, quarterly, monthly, daily).

If a loan lasts 12 years and is compounded quarterly, how many periods are there?

48

What should you use in TVM formulas when compounding is not annual?

periodic rate (r/m), total periods (n = m × y)

What does APR stand for?

Annual Percentage Rate (APR) is the stated interest rate, not accounting for compounding.

If you’re an investor, which compounding frequency is better?

More frequent compounding (monthly or daily).

If you’re a borrower, which compounding frequency is better?

Annual compounding (you pay less interest overall).

How are mortgage loans usually compounded?

Monthly.

How are credit cards typically compounded?

Daily.

How are savings accounts usually compounded?

Annually.

What does EAR stand for?

Effective Annual Rate, which reflects compounding effects and is used to compare rates.

How do you make a fair comparison between interest rates with different compounding?

Convert all rates to the EAR

What is an annuity?

A series of equal payments made at regular intervals over a finite period.

What are two types of annuities?

Ordinary annuity and annuity due (payment made at t=0)

What is a perpetuity?

A stream of equal cash flows that continues forever.

What is the formula for the present value of a perpetuity?

PV = C/r

Why are annuities important in finance?

They help with retirement planning, loan amortisation, insurance, and investment analysis.

How do you calculate the PV of uneven cash flows?

Add the present value of each individual cash flow

How do you calculate the present value of a cash flow received in the future (e.g., in year 3)?

Discount it back to today, PV= PV2/(1+r)²