Download Industrial Economics and Management and more Schemes and Mind Maps Industrial economy in PDF only on Docsity! 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. 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. Interest rate Formulas 1. Single-Payment Compound Amount 2. Single-Payment Present Worth Amount 3. Equal-Payment Series Compound Amount 4. Equal-Payment Series Sinking Fund 5. Equal-Payment Series Present Worth Amount 6. Equal-Payment Series Capital Recovery Amount 7. Uniform Gradient Series Annual Equivalent Amount 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-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. EXAMPLE-3: A person who is now 35 years old is planning for his retired life. He plans to invest an equal sum of Rs. 10,000 at the end of every year for the next 25 years starting from the end of the next year. The bank gives 20% interest rate, compounded annually. Find the maturity value of his account when he is 60 years old. The future sum of the annual equal payments after 25 years is equal to Rs. 47,19,810. Cash flow diagram of equal-payment series compound amount Equal-Payment Series Present Worth Amount • To find the present worth of an equal payment made at the end of every interest period for n interest periods at an interest rate of i compounded at the end of every interest period. 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 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. • Step-I • Step-II: The future worth sum of this revised series at the end of the 10th year is obtained as follows: This is equivalent to paying an equivalent amount of Rs. 5,691.60 at the end of every year for the next 10 years. At the end of the 10th year, the compound amount of all his payments will be Rs. 1,15,562.25. Example: Aloha Industrv
Table |
Initial outlay = Annual revenue Life
(Rs.) (Rs.) (years)
Technology | 12,00,000 400,000 10
Technology 2 2),00,000 6,00,000 10
Technology 3 18,00,000 3,00,000 10
