Interest rates payment

The same formula applies to the value of an annuity (PW) now, to provide for equal payments R at the end of each of n years, with interest rate 7,... 

A fourth method of computing depreciation (now seldom used) is the sinking-fund method. In this method, the annual depreciation A is the same for each year of the life of the equipment or plant. The series of equal amounts of depreciation Aq, invested at a fractional interest rate i and made at the end of each year over the life of the equipment or plant of s years, is used to build up a future sum of money equal to (Cpc S). This last is the fixed-capital cost of the equipment or plant minus its salvage or scrap value and is the total amount of depreciation during its useful life. The equation relating i Fc S) and Ao is simply the annual cost or payment equation, written either as... 

Short-Interval Compound Interest If interest payments become due m times per year at compound interest, mn payments are required in n years. The nominal annual interest rate Y is divided by m to give the effective interest rate per period. Hence,... 

Annual Cost or Payment A series of equal annual payments A invested at a fractional interest rate i at the end of each year over a period of n years may be used to build up a future sum of money E These relations are given bv... 

Equation (9-41) represents the future sum of a series of uniform annual payments that are invested at a stated interest rate over a period of years. This procedure defines an ordinaiy annuity. Other Forms of annuities include the annuity due, in which payments are made at the beginning of the year instead of at the end and the deferred annuity, in which the first payment is deferred for a definite number of years. 

The interest-rate equivalent of the cash discounts is 2 percent per month, since this discount could he obtained every month if payment were to he made at the beginning of the month rather than, as at present, at its end. Since the hills are settled monthly, the notional interest is paid monthly and should not he compounded. The discount is equivalent to 12 monthly simple-interest payments per year. Hence, from Eq. (9-31) the effective annual interest rate on discounts = (12)(0.02) = 0.24 = 24 percent. It would, therefore, he a good use of surplus cash to reduce this debt as quickly as possible. This would require cash equivalent to one-sixth of the annual hills due, or 16,700, to he avadahle. It can, therefore, he assumed that this level of liquidity is not available for capital projects, either as working capital to reduce the debt or for fixed-capital projects. Further, since the new project will not increase sales, it cannot generate further debt of this kind. Hence, this source is not available to capitahze the new project. 

X - payment per time period tl = number of periods i = interest rate per period... 

Calculate the monthly and yearly payments for obtaining a loan of 30,000 that is to be fully repaid in 20 years. Assume an interest rate of 8%. 

In the life insurance annuity a person contributes equal amounts over a number of years, and then at a given age (assuming he has not died previously) he receives a lump sum of money or some other form of payment. To determine how this compares with other forms of investment, the investor must determine at what interest rate his money would need to be invested in order to earn that lump sum in the same period of time. The first payment would earn compound interest for n periods. The second payment, which is made at the end of the first period, would earn interest for (n - 1) periods. The general rule is that each payment earns interest for one less period than the proceeding one. This can be expressed as... 

For corporations the same reasoning applies. To offer the prime interest rate the lender must be sure he can get his capital back plus interest. This means that the borrower s total assets must be considerably greater than the current liabilities and debts. Consider the simplified balance sheet given in Table 10-13. By current assets is meant cash and everything involved in working capital-feedstocks, unsold product, plus all the product that has been shipped but for which no payment has... 

A finance company gives the following figures For a loan of 1,000 a person must make 36 monthly payments of 38.62 per month. What is the rate of return What is the nominal interest rate ... 

What is the present value of the tax savings on the annual interest payments if the loan payments consist of five equal monthly installments of principal and interest of 3600 on a loan of 120,000. The annual interest rate is 14.0%, and the tax rate is 40%. (Assume the loan starts at the first of July so that only five payments are made during the year on the first of each month starting August 1.)... 

Hence WACC is applied two times in the model to calculate inventory capital costs and to discount period profits. This approach is used in payment plans, where interests for investments paid in each period are also discounted with an interest rate to calculate the net present value. 

The number e also appears in considerations of another form of growth, namely compound interest (i.e., the interest that accumulates when a principal P earns, and thereby grows from, successive payments at a fixed interest rate of i percent). The total principal after n periods (years in the case of many financial investments) can be determined by the following expression ... 

A less known but equally important impediment to stable environmental insurance markets (because of fhe long lag time between premium payment and damage claims) is erratic real interest rates. The political mismanagement of monefary and fiscal policy and fhe resulting inflation during the 1968-1979 period continue to affect real interest rates even today. 

Assume that the capital for the project is borrowed at 25% interest with a required return on investment of 5 years. Five annual payments are made to the creditors. The calculations made to determine the size of these payments and their repayment schedule are given in Appendix E (Table E.6). The five payments needed are each of AS5.02 million. These will cover both the 25% interest rate and the AS13.5 million principal. Operating and production costs are tax deductible as is the interest on borrowed capital, only gross profit is taxed. In the calculations, the AS5.02 million capital cost term is therefore broken into two components. The first is the tax-free interest component and the second must come from operating profit. This profit is assumed to attract 49% company tax. 

T = years before startup time that payment was made i = annual interest rate... 

The simplest form of interest requires compensation payment at a constant interest rate based only on the original principal. Thus, if 1000 were loaned for a total time of 4 years at a constant interest rate of 10 percent/year, the simple interest earned would be... 

The term (1 + i)" is commonly referred to as the discrete single-payment compound-amount factor. Values for this factor at various interest rates and numbers of interest periods are given in Table 1. 

Let R represent the uniform periodic payment made during n discrete periods in an ordinary annuity. The interest rate based on the payment period is i, and S is the amount of the annuity. The first payment of R is made at the end of the first period and will bear interest for n — 1 periods. Thus, at the end of the annuity term, this first payment will have accumulated to an amount of R(1 + i)n. The second payment of R is made at the end of the second period and will bear interest for n - 2 periods giving an accumulated amount of R( + Similarly, each periodic payment will give an additional accumu-... 

Solution. This problem is a typical case of an ordinary annuity. Over a period of 10 years, equal payments must be made each year at an interest rate of 6 percent. After 10 years, the amount of the annuity must be equal to the total amount of depreciation. 

Total amount of depredation = 12,000 — 2000 = 10,000 = S Equal payments per year = R = yearly cost due to depreciation Number of payments = n = 10 Annual interest rate = i = 0.06. 

The end-of-year convention is normally adopted for discrete interest factors (or for lump-sum payments) wherein the time unit of one interest period is assumed to be one year with interest compounding (or with lump-sum payments being made) at the end of each period. Thus, the effective interest rate is the form of interest most commonly understood and used by management and business executives. 

An original loan of 2000 was made at 6 percent simple interest per year for 4 years. At the end of this time, no interest had been paid and the loan was extended for 6 more years at a new, effective, compound-interest rate of 8 percent per year. What is the total amount owed at the end of the 10 years if no intermediate payments are made ... 

A concern borrows 50,000 at an annual, effective, compound-interest rate of 10 percent. The concern wishes to pay off the debt in 5 years by making equal payments at the end of each year. How much will each payment have to be ... 

R = end-of-year (or ordinary) annuity amount, dollars/year R = total of all ordinary annuity payments occurring regularly throughout the time period of one year, dollars/year r = nominal continuous interest rate, percent/100 5 = future worth, dollars... 

The assumptions of this study are premised on the commitment to a multi trillion dollar, centralized H2 production and delivery system in the U.S. over a thirty-year time period. Therefore, it is believed that the capital structure assumptions of 30% equity capital and 70% debt are more realistic for the assumed scale of capital investments. In addition, there are cash flow benefits to financing capital budgeting projects with debt capital rather than equity capital because interest on debt is tax deductible whereas dividends payments are not. The 7% interest rate for 30-year coupon bonds is a reasonable assumption for the assumed scale of investments, particularly so if a national H2 plan is adopted with government regulation and guaranteed bond issues. 

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