Question

Question 1 (50%): elaborate on the answers
a. You want to borrow money and the bank offers an annual interest rate of 7.3% compounded monthly. What is the equivalent Effective Annual Rate (EAR)? (10%)

b. A broker is presenting you with two different investment opportunities. Which one would you choose to invest it and why?
Opportunity A: Invest $13,000 today and receive $20,000 after 8 years from now.
Opportunity B: Invest in a financial instrument that will provide you with a 7.3% return per year for the same time period. (20%)

c. A fellow investor has invested $100,000 with a return of 5.3% for the next 5 years. You want to have the same profit as him/her but the available investment you can choose only offers 4% return. How much money should you invest in order to have the same profit as your fellow investor?

(20%

Answer 1

Calculation of effective annual rate:

annual rate=7.3% or .073

Effective annual rate=[(.073/12)+1]¹²-1

=1.0755-1

=.0755 or 7.55%

(b) Opportunity A:

13000(1+r)⁸=20000

(1+r)⁸=20000/13000

(1+r)=1.5385^{^(1/8)}

1+r=1.0553

r=1.0553-1

r=.0553 or 5.583%

Oppotunity B:

rate =7.3%

as the rate of return in oppotunity B is more than that in A therefore opportunity B is more benificial.

(C) future value (FV)of 100000 invested at 5.3% rate:

FV=100000*(1.053)^{^5}

FV=100000*1.2946

FV=129460

Gain=129460-100000

Gain=29460

Let amount to be invested by you be x.

x*(1.04)^{^5}=x+29460

x*1.2167=x+29460

.2167x=29460

x=29460/.2167

x=135948

hence amount to be invested =135948

Hence 135948 if invested at 4% rate will render a gain of 29453.53 which is approximately equal to 29461.86.

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