In an savings account, the principal is $1,800, has a #5 1/2%# annual interest rate, and is compounded quarterly. What is the amount in the account after 1 quarter?

1 Answer
Johnson Z.
Jan 31, 2016

#A=$1824.75#

Explanation:

Recall that the formula for compound interest is:

#A=P(1+i)^n#

where:
#A=#future value
#P=#principal (initial amount)
#i=#interest rate per compounding period, expressed as a decimal
#n=#number of compounding periods

Before we substitute our known values into the equation, we must first find the interest rate for one quarter. Recall that there are four quarters in a year, so we divide the annual interest rate, #5.50% (0.0550)#, by #4#:

#0.0550-:4#
#=0.01375#

Now that we know the interest rate per quarter, we can substitute our known values into the compound interest formula:

#A=P(1+i)^n#
#A=1800(1+0.01375)^1#
#A=$1824.75#

#:.#, the amount after one quarter is #$1824.75#.

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