Question

Please provide step by step solutions to these problems and not just the answer.

Only up to #23 is needed.

Math 342 16. Find the effective rate of interest corresponding to a nominal rate of 6%/year compounded 17. Find the present value of $41413 due in 5 years at an interest rate of 4.5%/year compounded 18. Find the payment R needed to amortize a loan of $22,000 at 3.5%/year compounded monthly 19. The manager of a money market fund has invested $4.2 million in CDs that pay interest at the quarterly quarterly with 36 monthly installments over a period of 3 years. rate of 5.4%/year compounded quarterly over a period of 5 years. How much will the investment be worth at the end of 5 years? 20. Andrew withdrew $5470.87 from a savings account which he closed this morning. The account had earned interest at the rate of 3%/year compounded continuously during the 3-year period that the money was on deposit. How much did Andrew originally deposit into the account? Chapter 6: 21. Maximize P-3x+5y subject to the constraints: 2x + 3y < 12;x +y <5;x 2 0;y 2 0 22. Minimize C- 2x+ 5y subject to the constraints: x + 3y 2 15;4x +y 2 16; x 2 0;y 20 23. An investor has decided to commit no more than $80,000 to the purchase of the common stocks of 2 companies A and B. She has also estimated that there is a chance of at most a 1% capital loss on her investment in Company A, and 4% loss on Company B. These losses should not exceed $2000. She also expects to make a profit of 14% on A and 20% on B. How much should she invest in each company to maximize her investment returns? What is that maximum return? Chapter 9 24. Find the indicated limit, if it exists. 3x2 +13x - 30 im 25. Find the slope and an equation of the tangent line to the graph of the function f at the specified point. f(x)=G+ (4,) at 26. Find the derivative of f (x) -7e2v*3 27. Find the derivative of g(x) 1000(7x2 - 3x + 4)1/2 Chapter 10 28. Find the intervals where the function is increasing/decreasing and concave upward/downward, and the relative extrema of f. f(x) -(4-x)e* 29. Find the absolute max and min values, if any, of the function: g(x) -x3 -x2+x+1 on [0,2]

Answer 1

Q16) Effectively rate of interest = (1 + stated interest rate/number of compounding periods)^ number of years - 1

Effectively rate of interest = (1+ (0.06/4))^(4*1) - 1 = 1.06136 - 1 = 0.06136 or 6.136%

Q17) Present Value = Future Value/(1+(r%/4))^(4*number of years)

Present Value = 41413/(1+(4.5%/4))^(4*5)

(note: we divide the rate of interest by 4 because we have to do compounding Quartly and multiply 1 by no of year because the period now increase)

Present Value = 41413/(1+(4.5%/4))^(4*5) = 41413/(1.01125)^20 = 41413/1.2507 = 33,111.85

Q18) EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

where P stands for the loan amount or principal, R is the interest rate per month and N is the number of monthly instalments

EMI = [22000 x (3.5%/12) x (1+3.5%/12)^36]/[(1+3.5%/12)^36 -1]

EMI = 71.26/0.1105 = $644.88

Q19) Future Value = Present Value*(1+(r%/4))^(4*number of years)

Future Value = $4.2 million *(1+(5.4%/4))^(4*5) = $4.2*(0.0135)^20 = $4.2*(1.3076) = $5.492 million

(note: we divide the rate of interest by 4 because we have to do compounding Quartly and multiply 1 by no of year because the period now increase)