Suppose Jose borrows $4,000 at an interest rate of 17% compounded each year assume that no payments are made on the loan find the amount owed at the end of 2 years
The formula to calculate compound interest is A = P*(1 + r/n)^(nt) where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years.
In this case, the interest is compounded yearly, so n = 1. Plugging in all the values, we get:
A = $4,000 * (1 + 0.17/1)^(1*2)
A = $4,000 * (1.17)^2
A = $4,000 * 1.3689
A = $5,475.60
So, Jose would owe $5,475.60 at the end of 2 years.
To find the amount owed at the end of 2 years, we can use the formula for compound interest:
A = P(1 + r)^n
Where:
A = amount owed
P = principal amount (initial loan amount)
r = interest rate (as a decimal)
n = number of compounding periods
In this case, Jose borrowed $4,000 at an interest rate of 17% compounded each year. We need to find the amount owed at the end of 2 years.
P = $4,000
r = 17% = 0.17
n = 2 (2 years)
Plugging these values into the formula, we have:
A = 4000(1 + 0.17)^2
Calculating the exponent first:
(1 + 0.17)^2 = 1.17^2 = 1.3689
Now, substitute the value back into the formula:
A = 4000(1.3689)
A = $5,475.60
Therefore, the amount owed at the end of 2 years is $5,475.60.