Jeremy is in Grade 8. He has a paper route and wants to save for his college education. He determines that he has $100 per month to put into an account at 6%/a compounded monthly. How much will he have at the end of five years for his college education?
n = 12 x 5 = 60
R = 100
I = 0.06/12 = 0.005
I know the answer is:
n = 12 x 5 = 60
R = 100
I = 0.06/12 = 0.005
= 100 ([1.005]^60 - 1)/.005
= 6977.00
But I have to draw a line diagram and I keep getting the following answers... I don't understand what i'm doing wrong. Can somebody please explain to me?
Time
(Years) Amount of money at the beginning of the year Interest for the year New amount of money by the end of the year
1 n/a n/a 1200$
2 1200$ 1200[0.6][12] = 86.40 1286.40$
3 1286.40$ 1286.40[0.6][12] = 92.62 1379.02$
4 1379.02$ 1379.02[0.6][12] = 99.29 1478.31$
5 1478.31$ 1478.31[0.6][12] = 106.44 1584.75$
In order to draw a correct line diagram, you need to understand the compound interest formula and how it applies to Jeremy's situation.
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the principal amount (initial amount of money)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
For Jeremy's situation:
P = $100
r = 6% (0.06)
n = 12 (compounded monthly)
t = 5 years
Using this information, we can calculate the final amount of money in Jeremy's account at the end of 5 years:
A = 100(1 + 0.06/12)^(12*5)
A = 100(1 + 0.005)^(60)
A ≈ $100(1.005)^60
A ≈ $179.08
Therefore, at the end of 5 years, Jeremy will have approximately $179.08 in his account for his college education.
I hope this clears up any confusion and helps you draw the correct line diagram.
It seems like you are trying to create a line diagram to represent the growth of Jeremy's savings over five years. However, the calculations you are using for the interest and the new amounts are not correct.
To correctly calculate the interest and the new amount each year, you need to use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (the initial amount of money) = $100
r = annual interest rate = 6% = 0.06
n = number of times the interest is compounded per year = 12 (compounded monthly)
t = number of years = 5
Using this formula, you can calculate the amount at the end of each year:
Year 1:
A = 100(1 + 0.06/12)^(12*1) = 106.17
Year 2:
A = 100(1 + 0.06/12)^(12*2) = 112.68
Year 3:
A = 100(1 + 0.06/12)^(12*3) = 119.51
Year 4:
A = 100(1 + 0.06/12)^(12*4) = 126.68
Year 5:
A = 100(1 + 0.06/12)^(12*5) = 134.20
So, using the correct calculations, the line diagram would look like this:
Time (Years) | Amount of money
1 | $106.17
2 | $112.68
3 | $119.51
4 | $126.68
5 | $134.20
Please note that these amounts represent the savings at the end of each year, not the interest earned during the year. To calculate the interest earned each year, you can subtract the principal amount (initial amount) from the new amount at the end of each year.