Laura borrows $5,000 at 10.5% compound. How much does she owe after 4 months?

1 Answer
Alan N.
Aug 26, 2016

A. Laura owes $5,177.31 at 10.5% p.a. after 4 months.

Explanation:

Although the question does not state the period over which the 10.5% rate applies, it's reasonable to assume 1 year - normally written #10.5% p.a.# (Per annum).

With that assumption, the rate per month #=r/12# so the compound interest fomula compounded monthly reduces to:

#A=P(1+r/12)^t#

Where: #P=$5,000#, #r=10.5%# and #t = 4# months
(In this example)

Hence: #A= 5000(1+10.5/(100*12))^4#

#= 5000(1+0.00875)^4#

#= 5000xx1.0352 = 5177.31# (to 2 decimals)

Laura therefore owes #$5,177.31# after 4 months.

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