Question

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.

Answer 1

Answer:

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