25 POINTS IF ANSWERED #1 You have just inherited $5,000 from an old, incredibly rich (and smart) math teacher. However there is one condition. You have to decide whether to put the money in an account with 9% annual percentage rate compounded yearly or an account with 8 % annual rate compounded quarterly (4 times each year) Each account will be compounded for 5 years. Which account would give you more money after the 5 years? Justify. How much money will the 9% account give you after 5 years? How much money will the 8% account give you after 5 years?
The amount of money that 9% account give you after 5 years is $7,828.41 and the amount of money will the 8% account give you after 5 years is: $7,429.74.
Compound interest is use to determine the principal amount including accumulated interest.
Yearly
P = $5000
r = 9% = 9/100 = 0.09
n = 12
t = 5 years
Hence:
A = 5000(1 + 0.09/12)^12 ×5
A = 5000(1 + 0.0075)^60
A = 5000(1.0075)^60
A = $7,828.41
Quarterly
P = $5000
r = 8% = 8/100 = 0.08
n = 4 compounded 4 times in a year.
t = 5 years
Hence:
A = 5000(1 + 0.08/4)^4 ×5
A = 5000(1 + 0.02)^20
A = 5000(1.02)^20
A = $7,429.74
Therefore the amount of money that 9% account give you after 5 years is $7,828.41 and the amount of money will the 8% account give you after 5 years is: $7,429.74.
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