Time Value of Money
The concept of the time value of money (TVM) is crucial for both investing and borrowing. It essentially states that a sum of money today is worth more than the same sum in the future due to its potential earning capacity. This principle applies whether the money is invested or borrowed.
Investing Money
If you invest money in a bank savings account, the amount you deposit today will grow over time due to interest. The accumulation of money over time is explained by the time value of money.
Borrowing Money
When you borrow money, the amount you owe increases over time due to interest. This increase also reflects the time value of money.
Key Terms
- Principal: The original amount of money invested or borrowed.
- Interest: The amount by which the principal increases over time.
- Rate of Interest (i): The interest amount expressed as a percentage of the principal per time period.
- Interest Period: The time duration over which the interest rate is applied (usually a year).
Calculating Interest
- Investment Example
- Principal: Rs.1,00,000
- Amount after 1 year: Rs.1,10,000
- Total Interest: Rs.1,10,000 – Rs.1,00,000 = Rs.10,000
- Rate of Interest per year: 10,0001,00,000×100=10%\frac{10,000}{1,00,000} \times 100 = 10\%1,00,00010,000×100=10%
- Loan Example
- Principal: Rs.1,50,000
- Amount after 1 year: Rs.1,62,000
- Total Interest: Rs.1,62,000 – Rs.1,50,000 = Rs.12,000
- Rate of the
Types of Interest
Simple Interest
- Definition: Interest is calculated only on the principal amount for each period.
- Formula: I T=P×n×i
- IT = Total interest
- P = Principal
- n = Number of periods
- i = Interest rate
Compound Interest
- Definition: Interest is calculated on the principal and also on the accumulated interest from previous periods.
- Formula: A=P(1+in)ntA = P \left(1 + \frac{i}{n}\right)^{nt}A=P(1+ni)nt
- A = Amount owed after time ttt
- P = Principal
- ii = Annual interest rate
- n= Number of times interest is compounded per year
- t = Number of years
Example of Simple vs. Compound Interest
Loan of Rs.10,000 for 5 years at 8% interest per year
- Simple Interest
- Annual Interest: Rs. 10,000 ×\times× 0.08 = Rs. 800
- Total Interest for 5 years: 5 ×\times× Rs. 800 = Rs. 4,000
- Total Amount Owed: Rs. 10,000 + Rs. 4,000 = Rs. 14,000
- Compound Interest
- Year 1: Interest = Rs. 10,000 ×\times× 0.08 = Rs. 800, Total = Rs. 10,800
- Year 2: Interest = Rs. 10,800 ×\times× 0.08 = Rs. 864, Total = Rs. 11,664
- Year 3: Interest = Rs. 11,664 ×\times× 0.08 = Rs. 933.12, Total = Rs. 12,597.12
- Year 4: Interest = Rs. 12,597.12 ×\times× 0.08 = Rs. 1,007.77, Total = Rs. 13,604.89
- Year 5: Interest = Rs. 13,604.89 ×\times× 0.08 = Rs. 1,088.39, Total = Rs. 14,693.28
Comparison
- Simple Interest: Total repayment = Rs. 14,000
- Compound Interest: Total repayment = Rs. 14,693.28
Conclusion
The time value of money shows how money grows over time due to interest. Simple interest calculates interest only on the principal, while compound interest calculates it on both the principal and accumulated interest, leading to higher returns or higher repayments over time.
