Given that the annual force of interest is 4.1% during the first 4 years and 5.6% thereafter, find the present value of a continuous payment stream at constant annual rate of £300 payable between times 3 and 10.
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- A deposit of $19,000 earns a continuous force of interest given by 0.028t for the first 5 years (t is time in years), and a constant force of 0.14 thereafter. What nominal quarterly compounding rate is earned over the first 13 years?Given an interest rate of 6.5 percent per year, what is the value at date t = 8 of a perpetual stream of $900 payments with the first payment at date t = 17?For total yearly payments of $10000 for 10 years, compare the compound amountaccumulated at the end of 10 years if the payments are (a) end-of-year, (b) weekly, c)dailyand d) continuous. The nominal (annual) interest is 20 percent and payments are uniform. I need to the part of d (continuous).
- A series of equal quarterly payments of $25,000for 10 years is equivalent to what future worthamount at an interest rate of 8.4% compounded atthe given intervals?(a) Quarterly(b) Monthly(c) ContinuouslyUsing an effective rate of interest of 8% per annum, calculate the CONVEXITY of the following series of payments: £300 payable after 4 years, £200 payable after 12 years, and £250 payable after 17 years.In a series of payments at the end of the period, the first payment is 240 TL and the second payment is 220 TL, decreasing by 20 TL each year compared to the previous year and continuing until it reaches 40 TL, and then continues as 40 TL forever. Calculate the cash value of this series of payments based on an annual effective interest rate of 8%.
- What is the present value of an investment in which the interest rate is 3.9% per year, compounded annually, with 6 regular withdrawals of $2500?For a sum of 1,050 to triple itself in 8 years and 6 months, what must be the rate of interest compounded semi-annually? (Finding the rate by linear interpolation)A series of equal quarterly payments of $6,000 for IO years is equivalent to what present amount at an interest rate of 12% compounded(a) quarterly?(b) monthly?(c) continuously?
- The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?An investment earns an annual interest rate of 12 percent compounded quarterly. What is the effective annual rate?A. 3.00%.B. 12.00%. C. 12.55% Use excelFind the present value of P1,200 due in 3 years and 9 months if money is worth 10%, compounded quarterly.
