You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest? a. Bank 1; 6.1% with annual compounding. b. Bank 2; 6.0% with monthly compounding. c. Bank 3; 6.0% with annual compounding. d. Bank 4; 6.0% with quarterly compounding. e. Bank 5; 6.0% with daily (365-day) compounding.

Option (d), Bank 4 offers the highest amount after a year

Explanation:

The total amount from each of the interest rates can be expressed as;

A=P (1+r/n) ^nt

where;

A=Future value of investment

P=Initial value of investment

r=Annual interest rate

n=Number of times the interest is compounded annually

t=number of years of the investment

a). Bank 1

P=x

r=6.1%=6.1/100=0.061

n=1

t=assume number of years=1

replacing;

A=x (1+0.061/1) ^ (1*1)

A=x (1.061)

A=1.061 x

b). Bank 2

P=x

r=6%=6/100=0.06

n=12

t=1

Replacing;

A=x (1+0.06/12) ^ (12*1)

A=x (1.005) ^12

A=1.0617 x

c). Bank 3

P=x

r=6%=6/100=0.06

n=1

t=1

Replacing;

A=x (1+0.06/1) ^ (1)

A=1.0600 x

d). Bank 4

P=x

r=6%=6/100=0.06

n=4

t=1

A=x (1+0.06/4) ^ (4*1)

A=x (1+0.015) ^4

A=x (1.061)

A=1.0614 x

e). Bank 5

P=x

r=6%=6/100=0.06

n=365

t=1

A=x (1+0.06/365) ^ (365*1)

A=1.0618

Option (d), Bank 4 offers the highest amount after a year