Suppose that you invest $10,000 in an account whose maturity is 5 years from now

Question

Suppose that you invest $10,000 in an account whose maturity is 5 years from now, and this is the only negative cash flow on your side. Also, assume that the annual interest rate on the account is 6%. Answer the following questions.

a. Derive cash flows that you receive during 5 years if payment is based on simple interest, and the payment is made at the end of each year.

b. Derive cash flows that you receive during 5 years if payment is based on simple interest, and the payment is made at the end of each 6 months.

c. Derive cash flows that you receive during 5 years if payment is based on simple interest, and the payment is made at the end of each quarter.

d. Derive the cash flow that you receive after 5 years if payment is based on annual compounding.

e. Derive the cash flow that you receive after 5 years if payment is based on semiannual compounding.

f. Derive the cash flow that you receive after 5 years if payment is based on quarterly compounding.

g. What conclusion can you make about the effect of compounding period on the cash flow? Provide your work in detail and explain. Provide references for the content. Provide your work in detail and explain. Provide references for the content.

Explanation / Answer

Simple int = Principal * Rate* Int. /100

S.I = Principal * rate/2*time /100

(c) S.I = 10000*(6/4)*(4*5)/100

= 3000

At the end of five year in all three option you will get $ 10000.

(D) Compund int. = Pincipal*(1+int.rate)^no. of years

= 10000*(1+.06)^5

= 10000*1.338226

= 13382.26

(E) In this part rate of int = .06/2 and no. of years = 5*2 = 10

then 10000*(1+.06/2)^10

= 10000*1.343916

= 13439.16

(f) Here in this part int rate = 6/4 as compouding will be done on quarterly basis and no. of years = 5*4 =20

= 10000*(1+.06/4)^20

= 10000*1.346855

= 13468.55

Cash flow will be higher if compunding will be done more in a year.

please note all values are in $.

In case of any clarification required please comment.

a) Year 0 1 2 3 4 5 Initial Deposit amt. 10000 Int./Cashflow amt 600 600 600 600 600

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