This week assignment required to solve three problems derived from our text book in a mathematical essay APA style format. First am going to start by solving all three problems and later putting in words explaining the steps used in solving the problems including all mathematical and describe how and why this is applicable to my everyday life. The first part of the problem request to rewrite the expression (P dollars is invested at annual interest rate r for 1 year. If the interest is compounded Semiannually, then the polynomial P (1+r/2)2 represents the value of the investment after1 year. And to also Evaluate the polynomial resulting from step 1 using P = $200 and r = 10%, and P = $5670 and r = 3.5% 1. First let me start with the first part of the question, which is rewriting the expression without parentheses. I am using the FOIL method by multiply the pairs: front, outside, inside, etc. P(1+r/2) ^2 The original expression P(1+r/2)*(1+r/2) A squared quantity multiplies itself P(1+r/2+r/2+r^2/2 The expression after FOIL was carried out P(1+r+r^2/4) Like terms are combined with r/2 + r/2 = r P+Pr+Pr^2/4 The P is distributed across the trinomial Usually traditional polynomials are in descending order of the variable r, but I notice that this one is in ascending order with the highest exponent in the last term instead of the first term. Now I can evaluate the first expression by plugging in P = $200 and r 10% = 0.1 interest rate as in decimal P+Pr+Pr2/4 the
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13. What is the formula for the Present Value (PV) for a finite stream of cash flows (1 per year) that lasts for 10 years?
What annual interest rate is needed to produce $200,000 after five years if only $100,000 is invested?
10. An investment of $1,000 today will grow to $1,100 in one year. What is the continuously compounded rate of return?
Therefore the annual interest rate is 8% and the effective annual rate compounded quarterly is 8.24%
Compute the incremental cash flows of the investment for each year. (Do not round intermediatecalculations. A negative answer should be indicated by a minus sign.)
The present value of an outlay in perpetuity for a particular project can be calculated as follows:
A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account? (Bluman, A. G. 2005, page 230).
The interest rate of a term deposit is at 5.2% per annum. Available investment fund is $200,000. Term Deposit will yield $10,400 p.a. by using $200,000 multiply by 5.2%. However, for compounded interest rate, 5 years investment will be $257,697 (ROI = $57,697). And 10 years investment will be $332,038 (ROI = $132,038), assume that the interest rate is constant within 10 years period. The risk is considered minimal.
Compounding monthly means that there are twelve interest payments per year. So, n = 12(5) = 60 and i = 0.08/12 = [pic]
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After the calculations you end up coming out with a rate of 14.87%. The third and final part of question three asks what rate you will need if the interest is compounded semiannually. All you have to do is double the amount of terms and you will come out with a lower number of 7.177%. Since the interest is compounded semiannually that means that you will need to times that number by two and you come out with your final number of 14.35%.
2(X4 + X5 + X6 + X7 + X10 + X11 + X16 + X17 + X18 + X27 + X28) – (X1 + X2 +X3
5. P = $40({1 – [1/(1 + .03)]26 } / .03) + $1,000[1 / (1 + .03)26]
We then get the annuity of the 1,200 semiannual PMTs at year 6, and then at Present Value