Question

64. Five years ago, Brian had invested $14,850 in a growth fund. The investment is worth $22,000 today. If the interest was compounded annually, what is the annual rate of return earned on the investment?

7.25%     
8.18%     
9.52%     
10.75%     
11.66%     

66. Bill is considering investing $450 at the end of every month in a fixed income instrument. He will be receiving $27,000 at the end of 4 years. If the interest is compounded monthly, what is the annual rate of return earned on the investment?

11.56%     
22.25%     
15.07%     
18.30%     
13.58%     

67. LeGo Financials offer two investment plans. Investment A pays 9 percent interest compounded monthly, whereas Investment B pays 10 percent interest compounded semiannually. What are the effective annual rates of the two investments?

9.38%; 10.50%     
9.38%; 10.25%     
9.75%; 10.25%     
9.75%; 10.50%     
9.94%; 10.45%     

69. A leading bank is coming up with an investment that pays 8 percent interest compounded semiannually. What is the investment's effective annual rate (rEAR)? Use a financial calculator to determine the amount.

8.16%     
8.36%     
8.56%     
8.76%     
8.96%     

Answer 1

64. Ans: 8.18%

Amount Invested 5 years ago= $ 14,850

Time Period = 5 years

Current Value of Investment = $ 22,000

Future Value = P (1+i)^n, where I = Interest Rate per Period, n= No. of periods

$ 22,000 = $ 14,850 (1+i)^5

(1+i)^5 = $ 22,000 / $ 14,850

(1+i)^5 = 1.4815

1+i = 1.4815^(1/5)

i = 0.0818 = 8.18%

66. Ans: 11.56%

Here Future Value of al the Payments should be equal to $ 27,000

$ 450 * FVAF(r%, (4*12 Months) = $ 27,000

Let us Verify with given Options:

Computation of FVAF(i%, n years)

i%	r = i/12	1+r	(1+r)^n	[(1+r)^n]-1	[(1+r)^n]-1 /r	F / (1+r)	$ 450 * G
A	B	C	D	E	F	G	H
11.56%	0.96%	1.0096	1.5844	0.5844	60.6644	60.09	27038.49114
22.25%	1.85%	1.0185	2.42	1.42	76.3362	74.95	33725.94566
15.07%	1.26%	1.0126	1.8204	0.8204	65.3271	64.52	29032.61179
18.30%	1.53%	1.0153	2.0678	1.0678	70.0197	68.97	31035.56017
13.58%	1.13%	1.0113	1.7163	0.7163	63.2960	62.59	28164.48254

As Amount is nearly equal to $ 27,000 in case of 11.56%, answe is11.56%.

67. Ans: 9.38%; 10.25%

Computation of Effective Rate of Interest:

Effective Rate of Interest = (1+i/n)^n - 1

where i = APR, n = Frequency of Compounding

Investment A:

Effective Rate of Interest = (1+0.09/12)^12 - 1

Effective Rate of Interest = (1.0075^12) - 1

Effective Rate of Interest = 1.0938 - 1

Effective Rate of Interest = 9.38%

Investment B:

Effective Rate of Interest = (1+0.10/2)^2 - 1

Effective Rate of Interest = (1.05^2) - 1

Effective Rate of Interest = 1.1025 - 1

Effective Rate of Interest = 10.25%

69. Ans 8.16%

Effective Rate of Interest = (1+0.08/2)^2 - 1

Effective Rate of Interest = (1.04^2) - 1

Effective Rate of Interest = 1.0816 - 1

Effective Rate of Interest = 8.16%