Question

Please explain how they got 2.25%

Suppose you are trying to save money for a vacation in two years. Bank A is offering savings account with annual interest rate 2%. You are pretty sure interest rates will go up and next year savings account will pay 2.5%. Bank B is offering a two-year time deposit (CD). That is, if you deposit money now you can't withdraw for 2 years. How much annual interest on time-deposit accounts should Bank B offer so that you are indifferent between putting your money at Bank A or at bank B? A) 4.5% B) 4% C) 2.5% D) 2.25%

Answer 1

Let P be the deposit amount

Let interest rate offered by Bank B is I%, then

F = P *(1+I)^t

F = P *(1+I)^2

Future worth of deposit in Bank A = P *(1+0.02) *(1+0.025) = P *(1.02) *(1.025) = P * 1.0455

As per condition given, both these deposits have to be equivalent, so

P * 1.0455 = P *(1+I)^2

(1+I)^2 = 1.0455

1+i = 1.0455 ^ (1/2) = 1.0224969

I = 1.0224969 - 1 = 0.0224969

I = 0.0225 = 2.25%

Therefore correct answer is option D