Consider a financial asset x which pays (10,10,10,110) at time t-(0.5, 1, 1.5,2). With respect to an interest rate term structure given by i(0,0.5) = 11.25%, i(0,1)= 11.50 % ,i(0,1.5) = 12.05%,i(0,2)= 12.70%, compute the duration of x.
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- Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? O FV = PV / (1+1)N O FV = PV + (PV XIX N) O FV = PV x (1 + I)N Simple interest? OFV = PV + (PV XIX N) O FV = PV XIX N O FV = PV/(PV XIX N)A. Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? FV = (1 + I)NN / PV FV = PV / (1 + I)NN FV = PV x (1 + I)NN B. Simple interest? FV = PV + (PV x I x N) FV = PV - (PV x I x N) FV = PV / (PV x I x N) C. Identify whether the following statements about the simple and compound interest methods are true or false. Statement True False After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest. All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound…Prove: FVA of an Ordinary Annuity times (1+i) = FVA of an Annuity Due, where i= interest rate. SHow all work
- If Po is the initial price of the security, P₁ is the price after you hold it for a year, and X represents a direct payment, an asset's rate of return is equal to: rate of return = (P₁ - Po) rate of return = (P₁ - Po) + X rate of return = (P₁-Po) / Po + XPo rate of return = (P₁ - Po)/Po + XTo find the present value (PV) of an ordinary annuity, a. the interest is compounded and then subtracted from the FV. O b. each payment is divided by (1+1)* c. each payment is multiplied by (1+1). O d. the future value (FV) is divided by the interest rate. e. the future value is divided by (1+1)*:For part d, told to manipulate the equation: ΔM(t)= rM(t)Δt M(t) represents the money value at time t E is the final value of the note r is the interest rate Δt is expiration minus today's date
- The Interest earned over a specified period of time is expressed a percentage of the original amount and is called rate of return. Select one: True False 21Choose the equation below that can be used to determine the value of "P" for a known interest rate, i.1) What is the future value at time t=3 for a present value of PV=$100 (e.g., t=0) if the interest rate is r=0.10 (e.g., r=10%)? 2) What is the future value at time t=18 for a present value of PV=$1525 (e.g., t=0) if the interest rate is r=0.085 (e.g., r=8.5%)? 3) What is the present value of a future value of FV=$500 at time t=5 if the interest rate is r=0.10 (e.g., r=10%)? 4) What is the present value for a future value of FV=$500,000 at time t=36 if the interest rate is r=0.05 (e.g., r=5%)? 5) What is the interest rate “r” if PV=$100 and the FV=$350 in year t=12? 6) What is the interest rate “r” if PV=$1250 and the FV=$2150 in year t=10? 7) How long will it take to double your investment if the interest rate is r=0.06 (r=6%)?8) How long will it take to increase your investment by 2.5 times if the interest rate is r=0.14 (r=14%)?9) Which is the better option if the interest rate is r=0.10 (r=10%)? Show all work used to arrive at your answer. a. Option I: Receive $1000 today at time…
- A competitive lender makes loans to a pool of borrowers that are identical. After borrowers have received their loans they choose one of two investment projects. with probability Pg. With probability 1 – Pg, Project G pays a rate of return of -1, the borrower defaults on the loan, and the lender receives Project G pays the borrower a rate of return of r. nothing. Project B pays the borrower a rate of return of rB with probability pp. And with probability 1 – Pb, Project B pays a rate of return of -1, the borrower defaults on the loan, and the lender receives nothing. Pb, and P,(1+ rg) > Po(1+ rb). Suppose rg 0.98, pr = 0.4, rp = 0.02, L = 1. We assume as usual that rg 0.10, rb 0.12, Pg %3D The lender can't distinguish between borrower types and so it charges all borrowers the same interest rate rL. The lender lends an amount L and pays interest rp on funds acquired from depositors. Round your answer to at least three decimal places.For each of the following situations, Identify (1) the case as either (a) a present or a future value and (b) a single amount or an annulty. (2) the table you would use in your computations (but do not solve the problem), and (3) the Interest rate and time periods you would use. (PV of $1, FV of $1, PVA of $1, and FVA of $1) Note: Use appropriate factor(s) from the tables provided. Round "Table Factors" to 4 decimal places. a. You need to accumulate $10,100 for a trip you wish to take in four years. You are able to earn 10% compounded semiannually on your savings. You plan to make only one deposit and let the money accumulate for four years. How would you determine the amount of the one-time deposit? b. Assume the same facts as in part (a) except that you will make semiannual deposits to your savings account. What is the required amount of each semiannual deposit? 1. You want to retire after working 40 years with savings in excess of $1,020,000. You expect to save $4,080 a year for 40…The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. P=$4000, r= 7.5%, t= 9 months The future value is $ (Simplify your answer. Type an integer or a decimal.)