**TIME VALUE OF MONEY | JAIIB AFM FREE NOTES**

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**TIME VALUE OF MONEY IMPORTANT TOPIC**

The time value of money is the principle that defines a sum of money as worth more now than the same will be at future date due to its earning potential as the money today can be invested and can be potentially grown into a larger amount in the future.

The future cash flow is divided by a discount factor that takes into account future time and anticipated interest rates to get the present value of the future cash flow.

The amount of cash multiplied by a function of the anticipated rate of return over the anticipated time period yields the future value of a sum of money today.

To determine whether to invest in a project or which cash flow sequence is most advantageous, for example, strategic, long-term financial decisions are made using the time value of money.

It generally ignores the inimical impact on the finance such as negative interest rates and capital losses. In case the losses seem to be unavoidable then the negative growth rates can be used.

For instance, Interest is accrued on funds deposited into savings accounts. The principal is increased over time by the interest, which increases the interest rate. The strength of compound interest is in this. The value of the money decreases over time if it is not invested.

**ANNUITIES **

Annuities are defined as a series of regular payments made over a period of time such as rent or car payments or have received a series of payments over a period of time.

**TYPES OF ANNUITIES**

ORDINARY ANNUITY |
ANNUITY DUE |

An ordinary annuity has payments due for either the inflow or outflow of funds at the conclusion of each period. belongs to the time frame before the date.
Payment For example, Housing loan |
The succession of cash flows that start off each period is referred to as annuity due. belongs to the time period post-date.
Receipts For example, life insurance premium |

**UNDERSTANDING THE FUTURE VALUE AND PRESENT VALUE OF AN ANNUITY **

**FUTURE VALUE: **The value of a group of recurring payments at a particular date in the future, presuming one specific rate of return, or discount rate is a future value

**PRESENT VALUE: ** The current value of the cash to be received in the future with one or more payments, which has been discounted at the market rate of interest.

**FUTURE VALUE OF ORDINARY ANNUITY**

FV (ordinary equity) = C [(1 + I) – 1 / I]

C = cash flow per period

I = interest rate

N = number of payments

**NUMERICAL**

**Mr ex opened an account with a bank to deposit Rs. 25000 by the end of each year at a 15% interest rate. How much would he get at the end of the 4****th**** year? **

FV (ordinary equity) = C [(1 + I) n – 1 / I]

25000 [ (1 + 0.15) -1/ 0.15 = 124666

Watch 19:39 https://youtu.be/bZaJ4ricoIY for the explained solution. |

**PRESENT VALUE OF AN ORDINARY ANNUITY**

PV of ordinary annuity = C[ ( 1+r)-1/ r(1+r)n]

C = Cash flow per period

r = discount rate

n = number of payments

**NUMERICAL**

**Sham opened an account with a bank to deposit Rs. 20000 at the end of each year at a 12% interest rate for 3 years. Guess the present value of the annuity.**

PV = C [ (1+r)-1/ r(1+r) n]

20000[ (1+0.12)3-1/0.12(1+0.12)3]

2.58

Watch 19:39 https://youtu.be/bZaJ4ricoIY for the explained solution. |

**FUTURE VALUE OF AN ANNUAL ANNUITY DUE**

FV of an annuity due = C [ (1+i) n – 1/i] x (1xi)

C = Cash flow per period

r = discount rate

n = number of payments

**How much interest would Geeta get at the end of the 5th year, if opened a recurring deposit account with a bank to deposit Rs. 100000 by the beginning of each year at a 10% interest rate?**

FV = C [ (1+i) n – 1/i] x (1xi)

100000 [ (1+0.10)-1/0.10] (1+0.10)

671000

**PRESENT VALUE OF ANNUITY DUE**

PV of annuity due = C [ (1+r) n-1/r(1+r) n] (1+r)

C = Cash flow per period

r = discount rate

n = number of payments

**Ram opened a recurring account with a bank to deposit Rs.50000 by the beginning of each year at a 10% interest rate for 3 years. Find the present value of the annuity.**

PV of annuity due = C [ (1+r) n-1/r(1+r) n] x (1+r)

50000 [ (1+0.10)3-1/ 0.10(1+0.10)3 x (1+r)

136400

**For more numerical-based questions refer to ****https://youtu.be/BjhR3zujV9I**

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