Question #8cdcd

2 Answers
Feb 13, 2018

the interest rate = 2.75%/year

Explanation:

Equation:
r = (1/t)(A/P - 1)

Solving our equation:
r = #(1/1)((2260.5/2200) - 1) #= 0.0275
r = #0.0275#

Converting r decimal to R a percentage
R = #0.0275 * 100#
R = #2.75%# per year

The interest rate required to get a total amount, principal plus interest, of $2,260.50 from simple interest on a principal of $2,200.00 over 1 years is 2.75% per year.

Feb 13, 2018

#2.76%#

Full explanation given.

Explanation:

#color(purple)("With practice you should be able to work these out in just a few")##color(purple)("lines.")#

The amount of interest earned is:

#$2260.50#
#ul($2200.00 larr" Subtract")#
#$color(white)("dd")60.50#

So as a fraction we have

#("amount gained")/("original amount") ->($60.50)/($2200.00)#

#color(blue)("First principle method")#

Percentage is just a fraction. However it is a special fraction in that the bottom number (denominator) is always fixed at 100.

With what follows notice the way the units of measurement ($) cancel out and we are left with just numbers.

So we need to change #(cancel($)60.50)/(cancel($)2200.00)# into:

#color(white)("ddddddddddddddd")("some number")/100#

How can we change 2200 into 100?

We can do this: #ubrace(2200xx1/2200)xx100=100#
#color(white)("ddddddddddddd")# becomes 1

In a fraction, for multiply and divide, what we do to the bottom we also do to the top. So we also have to multiply the top in the same way.

#60.50xx1/2200xx100 = 2.75#

#color(brown)("Putting it all back together")#

#(cancel($)60.50)/(cancel($)2200.00) -=2.75/100#

Note that #2.75/100# is the same as #2.75xx1/100# is the same as #2.75%#

So #%# is the same as #color(white)("ddd")xx1/100#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Shortcut method ")#

#color(brown)("In common with all shortcut methods, they are just")##color(brown)("remembering what happens with first principles")#

#(cancel($)60.50)/(cancel($)2200.00)->(60.5-:2200)xx100#

And then 'stick' a % on the end #->2.75%#