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plz help

thank you

 Mar 25, 2020
 #1
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+2

Hey guest! Let's start with some basic background knowledge of types of interest:

there are two main types, simple and compound. With simple interest, given a quantity:

\(x\), and in interest rate of \(r\%\) per year, we have that every year, the interest amount is:

\(x * r\%\). In other words, the amount paid every year(if we're talking about an interest on payment) is the exact same constant value.

 

Compound interest however, given the same variables, is a bit different.

Compound interest is "compounded"(hence the name) and added on to the previous year(or whatever metric of time used). The formula for compound interest is then typically defined:

\(A = P(1+\frac{r}{n})^{nt}\)

Where A = Amount paid

P = The principal, or the initial amount first paid 

R = Interest rate as a decimal

N = The number of times the interest is compounded per unit of time "t"

T = Time(in this example, years).

Here's a great website for reference on compound interest:

https://www.thecalculatorsite.com/articles/finance/compound-interest-formula.php

 

Getting to the problem itself:

A)

The interest that Sue gets with an investment of 2300 pounds and an interest rate of 2.4% a year over 3 years is:

\(A = 2300(1+\frac{0.024}1)^{3*1} = 2300(1.024)^3 = 2300(1.073741824) = 2469.6061952\)

For Bill, he invests 1800 pounds at an interest of 3.4% per year.

Our equation is then:

\(A = 1800(1+\frac{0.034}1)^{3*1} = 1800(1.034)^3 = 1800(1.105507304) = 1989.9131472\)

Of course, both of these answers are using calculators.

 

B)

 

To solve this, we figure out the compound interest for Bill after 2 years, and then multiply that amount by (1 + 0.04), which represents the 4 percent compound interest rate added on to that.

 

Sue:

We have already that Sue has an interest payment of 2469.6061952 after 3 years

 

Now, moving on to Bill:

By our previous formula:

\(\)

\(A = 1800(1.034)^2 = 1800(1.069156) = 1924.4808\)

We then multiply this value by 1.04 to represent a 4 percent interest rate(4% = 0.04, so 1+ 0.04 represents a 4 percent compounded interest).

\(1924.4808 * 1.04 = 2001.460032\)

Clearly, this is less than Sue's amount after 3 years, so the answer is then Sue

 Mar 25, 2020
 #2
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+1

Good work jfan17. However, you neglected something very important. The question is asking "Who gets more INTEREST after 3 years". So, you will have to subtract the principal from the calculated amounts in each category to see who earned the most INTEREST. I believe Sue has more interest in part "a" and Bill has more interest in part "b".

 Mar 25, 2020
 #3
avatar+485 
+1

Oh right! I was calculating the total amount after the given years(oops on my part) :P. Nice observation!

jfan17  Mar 25, 2020

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