Differentiate future value from present value and explain how compound interest
ID: 2759689 • Letter: D
Question
Differentiate future value from present value and explain how compound interest differs from simple interest. John expects to need $50,000 as a down payment on a house in six years. How much does she need to invest today in an account paying 7.25 percent? Richard is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years? What do you mean ratio analysis? Discuss important ratios used for analyzing financial statements. How do an ordinary annuity, an annuity due, and a perpetuity differ? Explain.Explanation / Answer
Answer – Q1
Future value is the amount one receives if an x amount is invested today at a rate of return of r for a period n. For example if one gets USD 100 after one year from now if he invests USD 75 today. Then USD 100 is the future value of the amount being invested.
Present value is the amount one needs to invest today if he is expecting X amount in future at an interest rate of r for a period n. For example, if one receives USD 100 after 1 year if an amount X is invested today at a rate 6% per annum, then the amount X is known as present value of the USD 100 which will be received after 1 year.
Simple interest is calculated for a period on a sum P. This amount will be same irrespective of the period for which the amount is held in multiples of the same period. Suppose one invests USD 100 for a period of 1 year at a rate of 5%, then he receives USD 100 * 1 * 5/100 = USD 5 as interest for one year. This interest amount will not change even if he invests for a period of 2 years or 3 years or even for 100 years.
Compound interest is the amount of interest on interest one receives as at the end of first compounding period the principal and interest earned for that period together will become the principal for the next compounding period. Continuing the earlier example, suppose it the investor invests USD 100 at 5% for 2 years under simple interests and invests a similar amount for 2 years under compounding interest, the amount received by him under the two methods will be as follows
Simple Interest
Interest for two years = USD 100 * 2 years * 5% = USD 10
(This is USD 5 interest per annum multiplied by 2 years USD 5 * 2)
Compound interest
First year - Interest amount - USD 100 * 1 year * 5% = USD 5
Second year - Principal USD 100 + USD 5 (interest earned for first year) = USD 105
Interest amount = USD 105 * 1 year * 5% = USD 5.25
This additional receipt of USD 0.25 is the interest on the interest received for the previous periods and is known as compound interest.
Answer Q2
Amount required for down payment = $50,000
Period after which the amount is required = 6 years
Rate of interest receivable in the account = 7.25%
Amount to be invested today to receive the amount =Amount receivable/(1+interest rate)^number of years
= $50000/(1+7.25%)^6
= $50000/(1.0725)^6
= $50000/1.5218918984
= $32,853.8446 or $32,853.85 (rounded off)
That is he need to invest $32,853.85 for 6 yaars at 7.25% rate of interest to receive $50,000.
Answer – Q3
Amount to be invested = $25000
Period of investment = 10 years
Rate of return = 8%
Value of investment after 10 years = $25000 * (1+8%)^10 years
= $25,000 * 1.08^10
= $25,000 * 2.1589249973
= $53,973.1249 or $53,973.13 (rounded off)
That is he received $53,973.13 in 10 years if he invests $25000 today at 8% rate of interest.
Answer – Q4
Ratio analysis is method of analysing financial statements of a business by deriving ratios of amounts invested / spent on various business activities against another set of amounts invested / earned / spent. These ratios are then compared over a period of time to check how the business is performing. There are several types of ratios like liquidity ratios, profitability ratios, operational ratios etc. Ratio analysis is also useful to compare two business with different sizes of financial statements as by calculating the ratios we can bring them to a common comparison factor.
Under liquidity ratios, current ratio is the most important one. This is calculated as Total Current Assets / Total current Liabilities. This ratio basically provides an idea about the short term liquidty of operations. If the ratio is less than 1, this indicates the firm needs to pay more in short term compared to what it owns in current assets.
Similarly net profit margin is another important ratio which is calculated as Profit After Tax / Sales. This ratio indicates how profitable the operations are. By comparing this ratio over a period of time we can see how the business is performing in terms of profitability
Turnover / Activity ratios indicates how efficiently funds invested in various activities are being utilized. Total Asset Turnover ratio is calculated as Net Sales / Total Assets. This ratio indicates how efficiently the total assets of the business are utilized in generating the revenues.
Answer Q5
Oridinary Annuity - This is an amount payable /to be paid at the end of a specific period for a pre-determined period of time. For example one receives an amount of USD 100 at the end of every month for next 10 years. This is known as ordinary annuity
Annuity Due - If the amount is received at the beginning of the period instead of at the end of the period then such annuity is known as annuity due. Taking the earlier example the person receives USD 100 at the beginning of the month for next 10 years, then such an annuity is known as annuity due.
Perpetuity is one where he/she receives or pays a pre-determined amount every period forever. That is say one receives an amount of USD 100 at the end of every month forever then that is known as a perpetuity.
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