# JavaScript Bond Calculator

The purpose of this calculator is to provide calculations and details for bond valuation problems.

It is assumed that all bonds pay interest semi-annually.

Future versions of this calculator will allow for different interest frequency.

**Instructions:** Fill in the spaces that correspond to the number of years, maturity, coupon rate, and yield-to-maturity,

followed by clicking on the "Compute" button.

The calculator will provide the rest.

The coupon rate and yield-to-maturity can be entered as whole numbers or in decimals.

Further business analysis samples of

Interest Rates and Bond Prices
### Future Value of Annuity

FV = C + C( 1 + r ) + C ( 1 + r )

^{2} + ... + C( 1 + r )

^{n - 1} = C [((1+r)

^{n}-1)/r]

where

**C** is the cashflow

and

**n** is the number of cashflows.

### Net Present Value of Annuity

NPV = C / (1 + r) + C / (1 + r)

^{2} + ... + C / (1 + r)

^{n} = C { 1 - [1/(1+r)

^{n}] / r }

where

**C** is the cashflow

and

**n** is the number of cashflows.

### Continuous Compounding

From compounding

**m** times per year to continuous compounding:

r

_{c} =

**m** * ln( 1 + r

_{m} / m )

From continuous compounding to compounding

**m** times per year:

r

_{m} = m( e

^{rc / m} - 1 )

#### Example

Interest Rate | 8% per annuum |

Compounding | Quarterly(4) |

r

_{c} = 4 * ln ( 1 + 0.08 / 4 ) = 0.0792 = 7.92%

Next, consider an interest rate that is quoted 12% per annum with continuous compounding.

The equivalent rate with annual compounding is

r

_{1} = 1 (e

^{0.12/1} - 1 ) 0.1275 = 12.75%

### Compounding Frequency

From compounding

**m** times per year to annual compounding:

r = (1 + r

_{m} / m)

^{m} - 1

From annual compounding to compounding

**m** times per annum:

r

^{m} = m * [ (1 + r)

^{(1/m)} - 1 ]

#### Example

Interest Rate | 8% per annuum |

Compounding | Quarterly(4) |

The equivalent rate with annual compounding is

r = ( 1 + 0.08 / 4 )

^{4} - 1 = 0.0824 = 8.24%

From

**m** to

**n** compoundings per annum:

The formula below can ber used to transform a rate r

^{n} with

*n* compoundings per year

to a rate r

^{m} with

*m* compoundings per year

r

^{n} = n * [ ( 1 + r

_{m} / m )

^{m/n} - 1 ]

#### Example

Consider a rate with compounding frequency four times per year.

If the rate is 7% then the equivalent rate with

*semiannual* compounding:

r

^{2} = 2 * [ ( 1 + 0.07 / 4 )

_{4/2} - 1 ] = 0.0706

The equivalent rate with

*semiannual* compounding is 7.06%