Question

three banks A,B and C, each offers a different effective interest rate on its saving account. Bank A nominal interest 8.25% compounding period daily, Bank B 8.25% compounding period monthly and Bank C 8. 30% compounding period quarterly. For each of the three banks find the effective semi-annual interest rate. Which bank would you prefer to invest your money in? with that bank, how much interest would you get after 3 years on $5000 deposit made now?What is the nominal interest rate for a bank that offers 1.4% interest rate every 2 months? Considering a new option bank D that offers 9% simple interest rate, would you prefer that bank over the one you chose in the another question

Answer 1

(1) Effective interest rate (EAR) = [1 + (r / m)]^m - 1, where

r: Nominal interest rate

m: Frequency of compounding in 6 months

(a) Bank A: r = 8.25%, m = 365/2 = 182 (taking integer value)

EAR = [1 + (0.0825 / 182)]¹⁸² - 1 = (1 + 0.0005)¹⁸² - 1 = (1.0005)¹⁸² - 1 = 1.0860 - 1 = 0.0860 = 8.60%

(b) Bank B: r = 8.25%, m = 6

EAR = [1 + (0.0825 / 6)]⁶ - 1 = (1 + 0.0138)⁶ - 1 = (1.0138)⁶ - 1 = 1.0854 - 1 = 0.0854 = 8.54%

(c) Bank C: r = 8.3%, m = 6/3 = 2

EAR = [1 + (0.083 / 2)]² - 1 = (1 + 0.0415)² - 1 = (1.0415)² - 1 = 1.0847 - 1 = 0.0847 = 8.47%

Since Bank A offers highest EAR, I will choose bank A.

(2) 3 years = (365 x 3) days = 1,095 days

Interest from bank A ($) = [5,000 x {1 + (0.0825 / 1,095)}^1,095] - 5,000 = [5,000 x {(1.0001)^1,095}] - 5,000

= [5,000 x 1.0860] - 5,000 = 5,430 - 5,000 = 430

(3) Nominal interest rate = 1.4% x (12/2) = 8.4%

(4) With bank D, interest on $5,000 for 3 years = $5,000 x 9% x 3 = $1,350

Since bank D offers higher total interest, I would choose bank D.