Question

Please, be neat and detailed. Explanations would be great. I need to understand it. Thank you.

Question 2 (18 points total). Consider the monthly cash flows shown in the diagram below. i=5% compounded weekly i=6% compounded continuously i=5.5% compounded monthly $650 $125 $125 $125 $125 $125 $125 0 1 2 3 4 5 6 7 8 9 10 months (a) (6 points) Find the effective interest rates for each of the three given nominal interest rates. Note: Present your answers as percentage with the appropriate suffixes. i=5.5% compounded monthly i-6% compounded continuously 1-5% compounded weekly Figure repeated from previous page for reference $650 $125 $125 $125 3 4 5 $125 $125 $125 7 8 9 10 months 0 1 2 6 (b) (12 points) Find the economic equivalence of this series at year 8, (ie, find V).

Answer 1

Compounding annually:-

Means that the amount would be compounded annually and interest would be calculated on the compounded amount. i.e if principle = 100, interest is 10% p.a, after one year amount would become =110[100+(100 x 10%)], and year two interest would be 11 (110 x 10%) and not 10% (100 x 10%).

Compounding monthly:-

Here the same annual compounding would be done at monthly frequency, i.e interest would be calculated per month and added to the amount after which interest would be calculated on that consolidated amount.

Same goes for weekly compounding and continuous (daily) compounding.

Thus, it should be clear that the higher the compounding frequency higher the interest.

Effective interest rate:

effective interest rate is the net rate at which interest is received annually.

EIR formula is  r = (1 + i/n)^n - 1 or e^i - 1

r represents the effective interest rate, i represents the stated interest rate, and n represents the number of compounding periods per year.

5.5% monthly :-

i = 0.055; n = 12;

EIR = 5.641 % per year.

5% weekly:-

i = 0.05; n = 52

EIR = 5.125% per year.

6% continuous:-

i = 0.06; n = 365

EIR = 6.183% per year