Question

question. 1) sted a lump sum 28 years ago at 4.05 percent annual interest. Today, he gave you the proceeds of that investment, totalling $48,613.24. How much did your father originally invest? A) $14,929.47 B) $16,500.00 C) $15,500.00 D) $15,994.70 E) $16,099.45 2)_ 2) Beginning three months from now, you will need $1,500 each quarter for the next four years to cover expenses. How much do you need to have saved today to meet these needs if you can earn.35 percent interest per quarter? A) $23,300.75 B) $26,069.79 C) $21,068.00 D) $22,319.54 E) $26,847.15 Tone 3) What is the EAR of 18.9 percent compounded continuously? A) 19.06 percent B) 19.89 percent C) 21.38 percent D) 19.43 percent E) 20.80 percent 4) 4) The current dividend yield on CJ's common stock is 1.89 percent. The company just paid an annual dividend of $1.56 and announced plans to pay $1.70 next year. The dividend growth rate is expected to remain constant at the current level. What is the required rate of return on this stock? A) 12.75 percent B) 13.39 percent C) 15.82 percent D) 9.08 percent E) 10.86 percent

Answer 1

1. Let the Amount Invested be PV

Interest Rate = r = 4.05%

Number of years = n = 28

Value of investment now = FV = $48613.24

=> FV = PV(1+r)ⁿ

=> PV = FV/(1+r)ⁿ = 48613.24/(1+0.0405)²⁸ = $15,994.70

2. Amount Invested at end of each quarter = P = $1500

Quarterly Interest rate = r = 0.35% = 0.0035

Number of Periods = n = 4*4 = 16 quarters

Present Value = PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ

= P[1- (1+r)^-n]/r

= 1500[1- (1+0.0035)^-16]/0.0035

= $23,300.75

3. Interest Rate = r = 18.9%

Time Period = t = 1 year

EAR = e^rt - 1 = e^0.189*1 - 1 = 0.2080 = 20.80%