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.

Bond Inputs Number of years to maturity Coupon rate Face value Yield to maturity BOND VALUE

Calculator Details Number of cash flows N Amount of cash flow PMT Yield per six months i Future value FV Solve for PV There are five variables in a bond valuation problem. Using a financial calculator requires that you type in the four known elements (N, PMT, I, and FV) and solve for the one unknown, the present value (PV). Computational Details Present value of interest Periodic cash flow Present value annuity factor Present value of face value Face value Discount factor The value a bond today is the sum of the present value of the interest payments (valued as an ordinary annuity) and the present value of the face value (discounted as a lump-sum): PV = [ S CFt/(1 + i)t] + [FV / (1 + i)t]

Conclusion

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^{r_c / 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
r₁ = 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 rⁿ with n compoundings per year
to a rate r^m with m compoundings per year
rⁿ = 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:
r² = 2 * [ ( 1 + 0.07 / 4 )_4/2 - 1 ] = 0.0706
The equivalent rate with semiannual compounding is 7.06%