Present Value of Compounded Value Formula

Present Value of Compounded Value Formula

Present value of compounded value can be calculated by the following simple formula

Present Value       = Compounded Value/e^rt

E=2.718

r= Rate of interest

t= compounding time

Example

Amount = 10,000

Compound interest= 12%

Period =3 Years

Compounded Value = 10,000x (1+12%)³=14049

Solution

Present Value       = Compounded Value/e^rt

=14,049/(2.718)^(.12)(3)

=14,049/(2.718)^.36

=14,049/1.4333

=9800

Compound Interest Doubling Time Formula

Compound Interest Doubling Time Formula

This following formula is used to calculate the period in which the amount would be doubled using the prevailing interested rate.

Doubling period Formula = ln(2)/r

r= interest Rate

Example

Interest rate =9%

Doubling Period?

Solution

Doubling Period Formula = ln(2)/r

=ln (2)/9%

=ln(2)/.09

=7.70 Years

It takes 7.7 years that an amount would be doubled. for example if 10,000 was invested ,then it would be 20,000 in 7.7 years.

Future Value of Growing Annuity Formula

Future Value of Growing Annuity Formula

There may be a growing series of payment deposited with institution to receive lump sum amount on maturity. Series of payment grow at gradual rate. The future value of such annuity may be calculated by following formula

Annuity Factor =Cx [(1+i)ⁿ-(1+g)ⁿ]

                                  i-g

i= interest Rate

g=Growth rate

n= period

C=Deposited amount

Example

Deposit = 10,000

Growth Rate of deposit = 5%

Interest Rate = 9%

Period =10 Years

Solution

Annuity Factor =10,000x [(1+9%)¹⁰-(1+5%)¹⁰]

                                            9%-5%

=10000 x [2.367 – 1.6288]/.09-.05

=184,550

Future Value of Annuity Due Formula

Future Value of Annuity Due Formula

Future value of annuity is calculated to determine the future value of the series of payment. This concept is widely used in insurance company.

Annuity Factor =Cx [(1+i)ⁿ-1] x (1+r)

                              i

Example

Amount Deposited= 2000

Period = 5 Years

Interest Rate =9%

Solution

Annuity Factor =C x [(1+i)ⁿ-1] x (1+r)

                               i

= Cx [(1+9%)⁵-1] x (1+9%)

           9%

=5.984 x 1.09

=6.5233

=6.5233 X 2000

=13,047

Money Interest Rate Formula

Money Rate Formula

Money Rate can be calculated from the real rate and inflation rate by fisher effect. It is important to note that money rate is roughly a sum of inflation rate & real rate.

(1+m) = (1+i)(1+r)

m=money rate

i= inflation rate

r= real rate

Example

Inflation rate in country = 5%

Real rate in country = 6%

Money Rate=?

Solution

(1+m) = (1+i)(1+r)

Money rate = (1.05)(1.06)-1

= (1.113)-1

=.071

=11.3%

Simple Interest Formula

Simple Interest Formula

Future value is calculated by the following simple formula

Future value = P ( 1+ Rn)

R= rate of interest

N = number of period

P = Present value

Simple Interest Formula Example

Bank is offering a simple rate of interest 12% (p.a) . Mr. A wants to deposit $ 25,000 today. How much amount Mr. A will received in 4 years?

Solution

= $ 25,000 (1+ .12x4)

=$ 25,000 x 1.48

=37,000

In simple interest the interest in not re invested therefore the interest amount remains same for each year.

Real Interest Rate Formula

Real Interest Rate Formula

Real rate does not include inflation rate, and can be calculated from money rate and inflation rate by using fisher effect formula. it is important to note that real rate is roughly money rate minus inflation rate, but exact rate can be calculated by fisher effect.

 (1+m) = (1+i)(1+r)

Re arrange formula

r         = (1+m)   -1

              (1+i)

m=money rate

i= inflation rate

r= real rate

Example

Prevailing Inflation rate = 8%

Money Rate in market = 12%

Money Rate=?

Solution

r        = (1+m)   -1

              (1+i)

r       = (1+12%) -1

              (1+8%)

=3.7% (Real Rate)

Interest Cover Formula

Interest Cover Formula

Interest cover ratio is calculated to know the company ability to pay interest. Interest cover ratio is calculated by following equation. Interest cover is expressed in term No of times. In other word it explains how much profit is available to pay interest.

Interest Cover =    Profit before Interest & Tax

                                      Interest

Example

Mr. Ali khan reported a Profit of $ 800,000 & interest is payable on debenture amount 10 million @ 4%. How much profit is available to pay interest?

Solution

Interest Cover =    Profit before Interest & Tax

                                        Interest

= $ 800,000/$ 400,000

=2 times

Equal Annual Return Formula

Equal Annual Return Formula

Equal annual return from a project may be calculated by applying annuity Factor. This concept has been explained with an example

Annual Return =         = Present Cash flow

                            Annuity Factor

  

Example

Project cost = 90,000

Term of project = 5 Years

Rate of Return = 12%

Calculate equal return from project?

Solution

Annuity Factor

= 1-(1.12)^-5

        .12

=3.6044

Annual Return

Annual Return =         = Present Cash flow

                        Annuity Factor

  

= 90,000/3.6044

=24,969

Effective Interest Rate Formula

Effective Interest Rate Formula

Effective Interest Rate is calculated with the help of following formula.

1+R= (1+i) ⁿ

R= Rate of Interest

I= Rate of interest for period (months, quarter, semiannual)

n= Number of periods (months, quarter, semiannual) in year

Example

A got a credit card from a reputable bank and bank offered him a 3% interest per months. Credit card amount was $ 10,000. Calculate the interest for the year?

R = (1+i) ⁿ-1

= (1.03)¹²-1

=1.4257-1

=.4257

= 42.57%

Interest amount = 10,000 x 42.57 %

=$ 4,257

Purpose of effective Interest Rate

Effective interest rate gives you annual interest cost and an effective tool to measure the different financial product. Effective interest rate takes into account the periodical compounding effect.

Compound Interest Formula

Compound Interest Formula

Compound interest is quite different from the simple interest. In compound interest the interest is not received by the investor each year , instead such interest is reinvested each year , therefore investor earn interest not only on principal amount but also on interest earn till the maturity.

Future value = P (1+r) ⁿ

P= Present Value

r= rate of interest

n= number of period

Example

Bank Deposit= 150,000

Rate of interest = 8%

Solution 

Future value = P (1+r)ⁿ

= $ 150,000(1.08)³

=$ 188,956.8

Interest for three years = future value – present value

= 188,956.8-150,000

=38,956.8

Future Annuity Present Value Formula

Future Annuity Present Value Formula

Present value of Future annuity may be calculated by the following formula

C x (Annuity Factor) x Discount Factor

Future Annuity Example

Annuity 50,000 ( 6-8)

Discount Rate = 5%

Solution

In first place we would determine the time line

0	1	2	3	4	5	6	7	8
						50,000	50,000	50,000

1.    Calculate the annuity at year 5

= 1-(1.05)^-3

        .05

=2.723

= $ 50,000 x 2.7232

=136160

2.    Discount the present value at year zero

0	1	2	3	4	5
					136,160

$ 136,160 x (1+.05)^-5

=$136,160 x .7835

=106,681

Tip of future annuity

One your discount for term of annuity i.e. 3 Year

Discount further for year Zero i.e. 5 Year

Total Discounting 3+5 =8 Years

Method 2

Annuity Factor 8 year      6.4632

Annuiy Factor 5 Year       4.3294

Annuity factor (6-8)         2.1338

50,000 x 2.1338

=106,690

Annuity Present Value Formula

Annuity Present Value Formula

Annuity present value is calculated for the investment decision. Annuity present value is the present value of future expected cash flows.

Present Value annuity = C x Annuity Factor

Where

Annuity Factor =1-(1+i)^-n

                          i

i=interest rate

n=number of periods

Example

50,000 for 5 Year

Cost of capital = 12%

Calculate annuity by short & long methods.

Solution

Annuity Factor

1-(1+i)^-n

     i

Where;

i=interest rate

n=number of periods

=1-(1+.12)^-5

       .12

=3.6047

PV of Annuity = 3.6047 x 50,000

180,238

Annuity Factor Formula

Annuity Factor Formula

Annuity Factor is used to calculate the present value of annuity. Annuity Factor can be calculated by following formula

Annuity Factor =1-(1+i)^-n

                          i

i=interest rate

n=number of periods

Example

Years= 4 Years

Interest Rate =14%

Calculate Annuity Factor

Solution

Annuity Factor =1-(1+i)^-n

                          i

Annuity Factor =1-(1+14%)^-4

                            i

=2.913

Labour Rate Variance Formula

Labour Rate Variance Formula

Labour rate variance is difference between the actual rate of actual labour and standard rate of actual labour. Labour rate variance may be favorable or adverse.  Labour rate variance can be calculated following equation or formula

Actual Quantity x (Actual rate- Standard Rate)

Example

Actual Labour on the production of Product X = 5000

Number of Unit produced of Product X = 1500

Standard Labour per unit of product X = 7 hr

Standard Rate = $6

Actual Labour Cost = 50,000

Calculate Labour rate Variance

Solution

Actual Cost per unit = 50,000/5000=10

Actual Quantity x (Standard Rate-Actual Rate)

= 5000 x (6-10)

= 5000 x -4

= -20000 (unfavorable)

Labour Efficiency Variance Formula

Labour Efficiency Variance Formula

Labour efficiency variance is calculated to show the labour performance. The difference between standard hour & actual hours is measured at standard rate. Labour efficiency ratio may be favorable or unfavorable. Labour efficiency variance can be calculated by the following formula

Actual > Standard hour = unfavorable Labour Variance

Actual Hours < Standard hour = Favorable Labour Variance

 Labour Efficiency Variance = (Standard Hours- Actual Hours) x (Standard Rate)

Example

 Table to be produced = 600

Standard Labour hour rate per table is= $ 6

Standard Labour hour needed per Table = 4 Hr

Actual hour taken was 1800 Hours

Calculate Labour Efficiency Variance

Solution

Standard Hours = 600 x 4 = 2400 hours

Labour Efficiency Variance = (Standard hours –Actual Hours) x (Standard Rate)

= (2400-1800) x 6

=(600 x6)

= 3600 (Favorable Variance)

Labour Efficiency Ratio Formula

Labour Efficiency Ratio Formula

Labour efficiency ratio is calculated by dividing the expected or standard labour hours with actual time taken by labour. This ratio explains the performance or efficiency of labour work force.

Labour Efficiency Ratio =   Expected Time.   x 100

                                        Actual Time

Example

Labour hour required for per unit production of equipment A = 8 Hours

Total Number of unit produced =400 units

Actual hour taken in production = 4000 Hour

Solution

Standard hours = 400 unit x 8 hr= 3200 hrs

Labour Efficiency Ratio =   Expected Time.   x 100

                                        Actual Time

=3200/4000 x 100

= 80% (Labour efficiency)

Labour efficiency has been 80%, which is 20% below than expectation