Question

which do you prefer: a bank account that pays 5.8% per year (EAR) for three years or

(a) An account that pays 2.7% every six months for three years?

(b) An account that pays 7.2% every 18 months for three years

(c) An account that pays 0.49% per month for three years

Answer 1

Number of years for deposited is held is 3 years. So we will calcuate Effective 3 year rate for all deposits and compare the rates.

First Pays 5.8% EAR for 3 years

annual rate (r) = 5.8%

number of compounding in 3 years or number of annual period in 3 years (m)= 3

Effective 3 year rate = ((1+r)^m)-1

=((1+5.8%)^3)-1

=0.184287112 or 18.43%

Second Pays 2.7% for 6 months

6 month rate (r) = 2.7%

number of compounding in 3 years or number of semiannual period in 3 years(m)= 3*2 = 6

Effective 3 year rate = ((1+r)^m)-1

=((1+2.7%)^6)-1

=0.1733367181 or 17.33%

Third pays 7.2% for every 18 months or 1.5 years

1.5 years rate (r) = 7.2%

number of compounding in 3 years or number of 1.5 yearly period in 3 years(m)= 2

Effective 3 year rate = ((1+r)^m)-1

=((1+7.2%)^2)-1

=0.149184 or 14.92%

Forth pays 0.49% per month

monthly rate (r) = 0.49%

Number of compounding or Number of monthly periods in 3 years = 3*12 = 36

Effective 3 year rate = ((1+r)^m)-1

=((1+0.49%)^36)-1

=0.1924013639 or 19.24%

Effective 3 year rate of option 4 is more that pays 0.49% per month for 3 years.

So we would choose  (c) An account that pays 0.49% per month for three years