Industrial Economics and Management, Schemes and Mind Maps of Industrial economy

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Interest rate formulas

Time value of Money

• (^) Since a rupee invested today is expected to be

worth more than a rupee in the future, the money

has earning power.

• (^) Due to this fact the worth of a rupee at a future

time is less than a rupee at the present time.

• (^) That means the same rupee is worth different

values at different time periods due to interest rate

and inflation.

• (^) Thus, interest is the manifestation of time value of

money.

 Simple interest rate is the interest is calculated, based on the initial deposit for every interest period.  Compound interest rate is the interest for the current period is computed based on the amount (principal plus interest up to the end of the previous period i.e., interest on interest) at the beginning of the current period. Interest rate

Important Notations to be Known P = principal amount; n = No. of interest periods; i = interest rate (It may be compounded monthly, quarterly, semi-annually or annually); F = future amount at the end of year n; A = equal amount deposited at the end of every interest period; G = uniform amount which will be added/ subtracted period after period to/ from the amount of deposit A1 at the end of period 1.

Single-Payment Compound Amount

• (^) To find the single future sum (F) of the initial payment (P) made at time 0 after n periods at an interest rate i compounded every period. Cash flow diagram of Single-Payment Compound Amount Formula to obtain the single-payment compound amount: Where, (F/P, i, n) is called as single-payment compound amount factor.

EXAMPLE-1: A person deposits a sum of Rs. 20,000 at the interest rate of 18% compounded annually for 10 years. Find the maturity value after 10 years.

P = Rs. 20,

i = 18% compounded annually

n = 10 years

F = P(1 + i)n^ = P(F/P, i, n)

= 20,000 (F/P, 18%, 10)

= 20,000 X 5.

= Rs. 1,04,

If Rs. 20,000 invested at 18% annual compounded interest

rate for 10 years then the deposit maturity value of the is

Rs. 1,04,680.

EXAMPLE-2: A person wishes to have a future sum of Rs. 1,00,000 for his son’s education after 10 years from now. What is the single-payment that he should deposit now so that he gets the desired amount after 10 years? The bank gives 15% interest rate compounded annually.

• (^) The person has to invest Rs. 24,720 now so that he will get a sum of Rs. 1,00,000 after 10 years at 15% interest rate compounded annually

Equal-Payment Series Compound Amount

• (^) To find the future worth of n equal payments which are made at the end of every interest period till the end of the nth interest period at an interest rate of i compounded at the end of each interest period.

Equal-Payment Series Sinking Fund

• To find the equivalent amount (A) that should be deposited at the end of every interest period for n interest periods to realize a future sum (F) at the end of the nth^ interest period at an interest rate of i. Cash flow diagram of equal-payment series sinking fund. In the above Figure, A = equal amount to be deposited at the end of each interest period n = no. of interest periods. i = rate of interest. F = single future amount at the end of the nth^ period. The formula to get F is where, (A/F, i, n) is called as equal-payment series sinking fund factor.

EXAMPLE-4: A company has to replace a present facility after 15 years at an outlay of Rs. 5,00,000. It plans to deposit an equal amount at the end of every year for the next 15 years at an interest rate of 18% compounded annually. Find the equivalent amount that must be deposited at the end of every year for the next 15 years. The annual equal amount which must be deposited for 15 years is Rs. 8,

EXAMPLE-5: A company wants to set up a reserve which will help the company to have an annual equivalent amount of Rs. 10,00,000 for the next 20 years towards its employees welfare measures. The reserve is assumed to grow at the rate of 15% annually. Find the single-payment that must be made now as the reserve amount. The amount of reserve which must be set-up now is equal to Rs. 62,59,300.

Equal-Payment Series Capital Recovery Amount

• (^) To find the annual equivalent amount (A) which is to be recovered at the end of every interest period for n interest periods for a loan (P) which is sanctioned now at an interest rate of i compounded at the end of every interest period

Uniform Gradient Series Annual Equivalent Amount

• (^) To find the annual equivalent amount of a series with an amount A1 at the end of the first year and with an equal increment (G) at the end of each of the following n – 1 years with an interest rate i compounded annually.

EXAMPLE-7: A person is planning for his retired life. He has 10 more years of service. He would like to deposit 20% of his salary, which is Rs. 4,000, at the end of the first year, and thereafter he wishes to deposit the amount with an annual increase of Rs. 500 for the next 9 years with an interest rate of 15%. Find the total amount at the end of the 10th year of the above series. Cash flow diagram of uniform gradient series annual equivalent amount.