Suppose that a loan of 6,500 is given at 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 2 years
To find the amount owed at the end of 2 years for a loan compounded annually, we use the formula:
A = P(1 + r/n)^(nt)
Where:
P = principal amount (the initial loan amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
For this question:
P = 6500
r = 7% = 0.07
n = 1 (since it is compounded annually)
t = 2
Substituting the values into the formula:
A = 6500(1 + 0.07/1)^(1*2)
= 6500*(1.07)^2
= 6500*1.1449
= $7446.85
So, the amount owed at the end of 2 years would be $7446.85.
To find the amount owed at the end of 2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount owed at the end of the time period
P = the principal amount (loan amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, we have:
P = $6,500
r = 7% or 0.07 (as a decimal)
n = 1 (compounded annually)
t = 2 years
Substituting these values into the formula, we have:
A = $6,500 * (1 + 0.07/1)^(1*2)
A = $6,500 * (1 + 0.07)^2
A = $6,500 * (1.07)^2
A = $6,500 * 1.1449
A ≈ $7,445.85
Therefore, the amount owed at the end of 2 years is approximately $7,445.85.