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

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

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