Carrie put $125 in an account for two years at 15% annual interest. How much money did Carrie have after two years?

2 Answers
Jan 11, 2018

Interest#->color(white)(".d.")$ color(white)("d") 37.50#
Deposit #->color(white)("d.")ul($125.00 larr" Add")#
Final sum #->$162.50#

Explanation:

#color(blue)("Preamble")#

The symbol % is a bit like a unit of measurement but 1 that is worth #1/100#

So #15%->15xx%->15xx1/100=15/100#

Thus we have #15/100xx$125# for 1 year

What follows is one way of working it out in your head (for #15/100#)

#15# is the same as #10+5# and #5# is #1/2" of "10#

So we have #10/100+5/100#

but #10/100 -=1/10#

so #5/100-=1/2xx1/10#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question using the above 'trick'")#

#1/10xx125=12.5#
#1/2xx12.5=ul(color(white)("d")6.25 larr" Add"#
#color(white)("DDDDDDD")18.75 color(white)("dddddddd")larr" this is "15/100xx125#

but the above is for 1 year. So for 2 years we have:

#2xx$18.75= $37.50# Interest
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question the traditional way")#

for 2 years we have 2 lots of #15/100xx$125# giving:

#2xx15/100xx$125#

#(3cancel(0))/(10cancel(0))xx$125#

#3xx1/10xx$125#

#3xx$12.50#

#$37.50# Interest

Jan 11, 2018

If it is simple interest, she has $162.50 after 2 years.
She has $165.31 after 2 years if the interest is compounded.

Explanation:

For simple interest use the formula

#color(white)(aaaaa)##I=Prt#

Where #I# is the interest accumulated
and #P# is the principal (amount invested)
#r# is the annual rate of interest
#t# is the time (in years if the interest rate is per year)

Substituting into the formula,
#I=Prt#
#I=(125)(0.15)(2)#
#I=37.50#

So with simple interest she has the amount she invested, $125, plus the interest she earned, $37.50, giving her a total amount of $162.50 in her account.

If the interest is compounded, use the compound interest formula

#color(white)(aaaaa)##A=P(1+i)^n#

#P##color(white)(aaaaa)#represents the principal (the money put in the account)
#A##color(white)(aaaaa)# represents the amount that has accumulated in the account at the end of the time period
#i# #color(white)(aaaaa)#represents the rate of interest at each compound
#n# #color(white)(aaaaa)#represents the number of times it is compounded (here once each year.)

So #P=125#
#A=?#
#i=15%##color(white)(aaa)##(15%=0.15)#
#n=2#

#A=P(1+i)^n#
#A=125(1+0.15)^2#
#A=125(1.3225)#
#A=165.3125#

Therefore she has $165.31 after 2 years using compound interest.

(We call this the PAIN formula)