Answer to Question #255700 in Financial Math for hghghh

Question

Suppose you want to open a bank account with 1463 Taka. After some research, you have narrowed down your choice to one of the two banks - bank X and bank Y. Both of them provide identical facilities except for yearly interest rate, r. Bank X pays with an interest rate rX=0.05 yearly (i.e. compounded 1 time per year), whereas bank Y pays an interest rate rY=0.03 at six months per year (i.e. compounded 2 times per year). Both banks use the following formula to calculate the annual (compound) interest amount, I=P(1+rn)n−P, where P denotes the principal (initial value), r is the interest rate, and n is the number of compoundings per year. So, your action set would be A={a1,a2}, where a1 means choosing bank X and a2 means choosing bank Y. Assume that the payoff function is defined as the yearly interest amount. Q1. What is the value of n for bank X? unanswered Q2. What is the value of n for bank Y? unanswered Q3. What is the annual interest amount paid by bank X?

Answer 1

Q1. Bank X pays with an interest rate 0.05 which is compounded 1 time per year hence value of n = 1 for Bank X

Q2. Bank Y pays with an interest rate 0.03 which is compounded 2 times per year hence value of n=2 for Bank Y

Q3. annual interest amount paid by Bank X is

$-P +P(1+0.05)^n$

where P is initial principal value P=1463 so interest by bank X is

$I_x = -1463 +1463(1+0.05)^1 = -1463 +1463 \times 1.05 = -1463 +1536.15 = 73.15 \\ I_x = 73.15$