Suppose that a loan of $6500 is given an interest rate of 7% compounded each year. Assume that no payments are made on the loan. Find the amount owed at the end of 1 year
The formula for compound interest is A = P(1 + r/n)^(nt) where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial loan)
r = annual interest rate (expressed as decimal)
n = number of times that interest is compounded per year
t = the time in years the money is invested for
In this case, the loan (P) is $6500, the interest rate (r) is 7% or 0.07, the interest is compounded once a year (n=1), and we're solving for the amount owed at the end of 1 year (t=1).
A = $6500 (1 + 0.07/1)^(1*1)
A = $6500 (1.07)^1
A = $6955
So, the amount owed at the end of 1 year would be $6955.
To find the amount owed at the end of 1 year, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan amount)
r = interest rate per period
n = number of compounding periods per year
t = number of years
In this case, the principal amount (P) is $6500, the interest rate (r) is 7%, the compounding periods per year (n) is 1, and the number of years (t) is 1.
Plugging these values into the formula, we get:
A = 6500 (1 + 0.07/1)^(1*1)
A = 6500 (1 + 0.07)^1
A = 6500 (1.07)^1
A = 6500 (1.07)
A = 6955
So, the amount owed at the end of 1 year is $6955.