Question

Which do you​ prefer: a bank account that pays 5.2 % per year​ (EAR) for three years or a. An account that pays 2.8 % every six months for three​ years? b. An account that pays 7.5 % every 18 months for three​ years? c. An account that pays 0.26 % per month for three​ years? ​(Note: Compare your current bank EAR with each of the three alternative accounts. Be careful not to round any intermediate steps less than six decimal​ places.)

If you deposit $1 into a bank account that pays 5.2 %per year for three​ years:

The amount you will receive after three years is $ (Round to five decimal​ places.)

a. An account that pays 2.8 % every six months for 3​ years? If you deposit $ 1into a bank account that pays 2.8 %every six months for three​ years:

The amount you will receive after three years is ?. ​(Round to five decimal​ places.)

b. An account that pays

7.5 %7.5%

every 18 months for 3​ years?                                         

If you deposit$ 1into a bank account that pays 7.5 %every 18 months for three​ years:

The amount you will receive after three years is ​$ ​(Round to five decimal​ places.)

An account that pays 0.26 % per month for three​ years?If you deposit $1 into a bank account that pays 0.26 % per month for three yearsThe amount you will receive after three years is (Round to five decimal​ places.)

Answer 1

(a) If you deposit $1 into a bank account that pays 5.2 % per year for three​ years, the amount you will receive after three years is

$1 * (1 + 0.052)^3 ==> $1.16425

(b) If you deposit $1 into a bank account that pays 2.8 % every six months for three​ years, the amount you will receive after three years is : $1 * (1 + 0.028)^6 ==> $1.18021. In 3 years, there are 36 months. As interest is paid every 6 months, there are (36 / 6) periods. Hence there are 6 compounding periods.

(c) If you deposit $1 into a bank account that pays 7.5 % every 18 months for three​ years, the amount you will receive after three years is ​$1 * (1 + 0.075)^2 ==> $1.15563.  In 3 years, there are 36 months. As interest is paid every 18 months, there are (36 / 18) periods. Hence there are 2 compounding periods.

(d) If you deposit $1 into a bank account that pays 0.26 % per month for three year, the amount you will receive after three years is $1 * (1 + 0.0026)^36 ==> $1.09799.  In 3 years, there are 36 months. As interest is paid every 1 months, there are 36 compounding periods.

The most preferred option is (b) as it gives the highest future value of $1.18021