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?
amount = payment [(1+i)^n - 1]/i
where i = .06/12 = .005
n = 5(12) = 60
payment = 100
To calculate how much Jeremy will have at the end of five years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
From the information given, we know that:
P = $100 per month = $100 * 12 = $1,200 per year
r = 6% = 0.06 (as a decimal)
n = 12 (compounded monthly)
t = 5 years
Substituting these values into the formula, we get:
A = $1,200(1 + 0.06/12)^(12*5)
Simplifying the exponent:
A = $1,200(1 + 0.005)^(60)
Calculating the value inside the parentheses:
A = $1,200(1.005)^(60)
Using a calculator or spreadsheet, we can evaluate (1.005)^(60):
A = $1,200(1.34872)
Calculating the final amount:
A = $1,618.46
Therefore, at the end of five years, Jeremy will have approximately $1,618.46 saved for his college education.