Which do you prefer: a bank account that pays 5.5% per year (EAR) for three year
ID: 2820721 • Letter: W
Question
Which do you prefer: a bank account that pays 5.5% 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 7.2% every 18 months for three years? C. An account that pays 0.43% per month for three years? (Note: Compare your current bank EAR with each of the three altemative accounts. Be careful not to round any intermediate steps less than six decimal places.) If you deposit $1 into a bank account that pays 5.5% 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 $1 into a bank account that pays 2.8% every six months for three years: The amount you will receive after three years is s .(Round to five decimal places.) Which bank account would you prefer? b. An account that pays 7.2% every 18 months for 3 years? If you deposit $1 into a bank account that pays 7.2% every 18 months for three years: The amount you will receive after three years is $. (Round to five decimal places.) Which bank account would you prefer? C. An account that pays 0.43% per month for three years? .(Select from the drop-down menu.) . (Select from the drop-down menu.) Enter your answer in each of the answer boxes,Explanation / Answer
Requirement: 1
We can compare the savings plan computing effective annual rate as:
r = (1+i/n) n – 1
r = Effective annual interest rate
i = Stated annual interest rate
n = No. of compounding periods in a year
a.
EAR of 2.8 %, compounded semiannually = (1+ 0.028)12/6 – 1 = (1.028) 2 – 1
= 1.056784 -1 = 0.056784 or 5.68 %
As the EAR is higher, 2.8 %, compounded semiannually is preferable than 5.5 % annually.
b.
EAR of 7.2 %, compounded 18 monthly = (1+ 0.072)12/18 – 1 = (1.072) 0.666666667 – 1
= 1.047441693 - 1 = 0.047441693 or 4.74 %
5.5 %, annually is preferable as the EAR of 7.2 %, compounded 18 monthly is less than, 5.5 %.
c.
EAR of 0.43 %, compounded monthly = (1+ 0.0043)12/1 – 1 = (1.0043) 12 – 1
= 1.052838002 -1 = 0.052838002 or 5.28 %
5.5 % , annually is preferable as the EAR of 0.43 %, compounded monthly is less than, 5.5 %.
Requirement: 2
Formula of compound interest is:
A = P x (1 + r/m) m x t
A = Future value of investment
P = Principal
r = Rate of interest
m = No. of compounding in a year
t = No. of years
A = $ 1 x (1 + 0.055/1) 1x3
= $ 1 x (1.055) 3
= $ 1 x 1.174241375
= $ 1.174241375 or $ 1.1742
Amount received after 3 years is $ 1.1742
a.
A = $ 1 x (1 + 0.028) 2x3
= $ 1 x (1.028) 6
= $ 1 x 1.180208364
= $ 1.180208364 or $ 1.1802
Amount received after 3 years is $ 1.1802
2.8 % semiannually is preferable.
b.
A = $ 1 x (1 + 0.072) 0.666666667x3
= $ 1 x (1.072) 2
= $ 1 x 1.149184
= $ 1.149184 or $ 1.1492
Amount received after 3 years is $ 1.1492
5.5 % annually is preferable.
c.
A = $ 1 x (1 + 0.0043) 12x3
= $ 1 x (1.0043) 36
= $ 1 x 1.167037085
= $ 1.167037085 or $ 1.1670
Amount received after 3 years is $ 1.1670
5.5 % annually is preferable.
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