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The need for day count conventions is a direct consequence of interest-earning investments. Different conventions were developed to address often conflicting requirements, including ease of calculation, constancy of time period (day, month, or year) and the needs of the accounting department.
WAL should not be confused with the following distinct concepts: Bond duration Bond duration is the weighted-average time to receive the discounted present values of all the cash flows (including both principal and interest), while WAL is the weighted-average time to receive simply the principal payments (not including interest, and not discounting).
The formula to calculate the interest is given as under = (+) = (+) where I is the interest, n is time in months, r is the rate of interest per annum, and P is the monthly deposit. [ 4 ] The formula to calculate the maturity amount is as follows: Total sum deposited+Interest on it = P ( n ) + I {\displaystyle ={P(n)}+I} = P ∗ n [ 1 + ( n + 1 ...
The average duration of the bonds in the portfolio is often reported. The duration of a portfolio equals the weighted average maturity of all of the cash flows in the portfolio. If each bond has the same yield to maturity, this equals the weighted average of the portfolio's bond's durations, with weights proportional to the bond prices. [1]
To extract the forward rate, we need the zero-coupon yield curve.. We are trying to find the future interest rate , for time period (,), and expressed in years, given the rate for time period (,) and rate for time period (,).
The formula for calculating 30-day yield is specified by the U.S. Securities and Exchange Commission (SEC). [1] The formula translates the bond fund's current portfolio income into a standardized yield for reporting and comparison purposes.
Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
The present value formula is the core formula for the time value of money; each of the other formulas is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations. The present value (PV) formula has four variables, each of which can be solved for by numerical methods: