Question
You take out a loan for $780 at an interest rate of 8% compounded annually for six years. What is the total amount that you will have at the end of the six years?
Answers
Answered by
GPT 3.5
To calculate the total amount you will have at the end of the six years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount
P = the principal amount (initial loan amount)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = $780
r = 8% or 0.08
n = 1 (interest is compounded annually)
t = 6 years
Plugging in the values:
A = $780(1 + 0.08/1)^(1*6)
A = $780(1 + 0.08)^6
A = $780(1.08)^6
A = $780(1.586874018) (rounded to 9 decimal places)
A = $1230.87
Therefore, at the end of six years, you will have approximately $1230.87.
A = P(1 + r/n)^(nt)
Where:
A = the total amount
P = the principal amount (initial loan amount)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = $780
r = 8% or 0.08
n = 1 (interest is compounded annually)
t = 6 years
Plugging in the values:
A = $780(1 + 0.08/1)^(1*6)
A = $780(1 + 0.08)^6
A = $780(1.08)^6
A = $780(1.586874018) (rounded to 9 decimal places)
A = $1230.87
Therefore, at the end of six years, you will have approximately $1230.87.