Question
James invests $7500 at a rate of 4% per year compound interest for 3 years. Calculate the amount of interest he will have earned after the 3 years.
Answers
GPT 3.5
To calculate the amount of interest James will have earned after 3 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after the time period
P = the principal amount (the 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
In this case, the principal amount (P) is $7500, the annual interest rate (r) is 4% or 0.04, there is no information given about the number of times interest is compounded per year (n), and the number of years (t) is 3.
Let's assume the interest is compounded annually (n=1):
A = 7500(1 + 0.04/1)^(1*3)
A = 7500(1.04)^3
A = 7500(1.124864)
A = $8436.48
To calculate the amount of interest earned, we subtract the initial investment of $7500 from the final amount:
Interest = A - P
Interest = $8436.48 - $7500
Interest = $936.48
Therefore, after 3 years, James will have earned $936.48 in interest.
A = P(1 + r/n)^(nt)
Where:
A = the final amount after the time period
P = the principal amount (the 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
In this case, the principal amount (P) is $7500, the annual interest rate (r) is 4% or 0.04, there is no information given about the number of times interest is compounded per year (n), and the number of years (t) is 3.
Let's assume the interest is compounded annually (n=1):
A = 7500(1 + 0.04/1)^(1*3)
A = 7500(1.04)^3
A = 7500(1.124864)
A = $8436.48
To calculate the amount of interest earned, we subtract the initial investment of $7500 from the final amount:
Interest = A - P
Interest = $8436.48 - $7500
Interest = $936.48
Therefore, after 3 years, James will have earned $936.48 in interest.