# Time Value of Money

Time value of money

Which would you prefer -- \$1000 today or \$1000 in 4 years?
Certainly, \$10,00 today.
Your response motivated by the ‘Time value of money’
You already recognized that there is TIME VALUE TO MONEY!!

Significance of TIME
Why is TIME such an important element in your decision?
TIME allows you the opportunity to postpone consumption and earn INTEREST

Interest
Interest is a return on a deposit. Interest paid on the principal borrowed is simple interest. Interest paid on any previous interest, as well as on the principal borrowed is compound interest.

Simple Interest
Assume that you deposit \$10,000 in an account earning 5% simple interest for 4 years.   The accumulated interest at the end of the 2nd year can be calculated using the formula:

SI = P0 (i) (n)

SI: Simple Interest
P0: Deposit today (t=0)
i: Interest Rate per Period
n: Number of Time Periods

SI = \$10,000 (0.05) (4) = \$2,000
The simple interest on the deposit of \$10,000 for 4 years @ 5% is \$2000.

Compound Interest
How is compound interest different from simple interest? Shierly Winters deposits \$10,000 @ compounded interest rate of 5% per annum for 4 years. She wants to know how much it will becomes after 4 years.

She earned \$500 interest on your \$10000 deposit over the first year. This is the same interest you would earn under simple interest. In the second year the interest would be

FV1 = P0 (1+i)1 = \$10,000 (1.05) = \$10,500
FV2 = FV1 (1+i)1
= P0 (1+i)(1+i) = \$10,000(1.05)(1.05)
= P0 (1+i)2 = \$10,000(1.05)2 = \$11,025
In the second year she earned an interest of Rs.525 as interest. The EXTRA \$25 is the compound interest over simple interest. Accordingly, the future value at the end of the 4th year would be
= P0(1+i)(1+i)(1+i)(1+i) = \$10,000(1.05)(1.05)(1.05)(1.05)

This is equivalent to P0 (1+i)4 = \$12,155
= \$10,000 (1.05)4 = \$12,155
The formula is:   FV = PV(1+i)n
Her deposit of \$10000 grows to \$12155 at the end of the fourth year....