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 one year
The amount owed at the end of one year can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where:
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per unit time
- t is the time in years
In this case:
- P = $4000
- r = 17% = 0.17 (in decimal form)
- n = 1 (because the interest is compounded yearly)
- t = 1 (because we want to find the amount owed at the end of one year)
Plugging these into the formula gives:
A = $4000(1 + 0.17/1)^(1*1) = $4000(1.17) = $4680
So Jose will owe $4680 at the end of one year.
To find the amount owed at the end of one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money after time t,
P is the principal amount (initial loan amount),
r is the annual interest rate (as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.
In this case, Jose borrows $4,000 at an interest rate of 17% compounded each year, and the loan is for 1 year. Therefore:
P = $4,000,
r = 17% = 0.17,
n = 1 (compounded annually), and
t = 1.
Plugging these values into the formula, we can calculate the amount owed after one year:
A = $4,000(1 + 0.17/1)^(1*1)
A = $4,000(1 + 0.17)^(1)
Calculating within the parentheses first:
A = $4,000(1.17)^(1)
A = $4,000(1.17)
A = $4,680
Therefore, the amount owed at the end of one year is $4,680.