Financial Mathematics → Annuities Payable at Intervals Annuities Payable at Intervals of Time. When we have interest rate per annum convertible to quarterly. Example 1. An investor wants to purchase a level annuity of 190 pounds per annum payable monthly in arrears for 6 years. Find the purchase price, given that it is calculated on the […]

# Internal Rate of Return

Financial Mathematics → Internal Rate of Return The internal rate of return (IRR) or the discounted cash flow rate of return is the rate of return that makes Net Present Value (NPV) is equal to zero. Example 1. An investor is considering a project which requires an outlay of 3 million pounds initially, and another outlay […]

# Rate of Interest Convertible Fractionally

Financial Mathematics → Rate of Interest Convertible Fractionally If we have annual discount rate , then what is the effective annual rate of discount for the period 1/p. Example 1. If we have rate of discount of 2.7% per annum convertible monthly. What is the effective annual rate of discount? Solution As we know that the […]

# Effective Interest Rate

Financial Mathematics → Effective Interest Rate The relation between Effective Rate of Interest and the Force of Interest. We know that the Interest Earned is calculated by the formula: In case of Effective interest rate and the force of interest, the Interest Earned is calculated by the formula Interest Earned = Investment × Effective Rate of Interest […]

# Theorem: Accumulation Factor

Financial Mathematics → Theorem: Accumulation Factor Accumulation Factor and Force of Interest Theorem. If δ(t) and A(t0,t) are continuous functions of t and t≥t0, and the principle of consistency holds, then, for t0≤t1≤t2 Example 1. Assume that δ(t), the force of interest per unit time at time t, is given by: (a) δ(t) = δ (b) δ(t) = a+bt Find formulae […]

# Force of Interest

Financial Mathematics → Force of Interest In basis for continuous interest we noted that as h becomes smaller and smaller, ih(t) tends to a limiting value, say δ(t) Mathematically, And, as We can also define δ(t) in terms of accumulation factor

# Principle of Consistency

Financial Mathematics → Principle of Consistency According to the principle of consistency For example, Example 1. For all prove that the principle of consistency holds for the accumulation factor Solution: Let , then for the principle of consistency we have to show that We have So, Hence, So, the principle of consistency is proved.

# Accumulation Factor Ratio

Financial Mathematics → Accumulation Factor Ratio In Accumulation Factor we obtained the formula In general, Example 1. Let time be counted in years. $5000 are invested at time 0 and the proceeds at time 10 are $9000. Calculate A(6,10) if A(0,9)=1.8, A(2,4)=1.1, A(2,6)=1.32, and A(4,9)=1.45. Solution: We have to calculate

# Accumulation Factor

Financial Mathematics → Interest → Simple Interest → Compound Interest → Continuous Interest → Accumulation Factor In Interest for different compounding periods, we have the formula for accumulated amount Where is called accumulation factor. So, an investment for a term h from time t to time t+h has accumulation factor Where, is called effective rate of interest per annum, and […]

# Continuous Interest

Financial Mathematics → Interest → Simple Interest → Compound Interest → Continuous Interest The basis for continuous compound interest. See the following example to know the basis for continuous interest. Example 1. Suppose $1,000 is deposited in a savings account that earns compounded interest at a rate of 10% per year. How much will be in the account after […]