Goran borrowed 8000at a rate of 7%, compounded semiannually. Assuming he makes no payment, how much will he owe
$54,922
But he's gonna get his legs broken long before the bill is that high.
To calculate the future value of a loan compounded semiannually, we can use the compound interest formula:
Future Value (FV) = Principal (P) * (1 + (rate/n))^ (n*t)
Where:
- Principal (P) is the initial amount borrowed
- Rate is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, Goran borrowed $8000, the interest rate is 7% (0.07 in decimal form), and it is compounded semiannually (twice a year). Let's assume he borrowed for a period of one year.
Principal (P) = $8000
Rate = 7% or 0.07
n = 2 (compounded semiannually)
t = 1 (borrowed for one year)
Plugging these values into the formula:
FV = $8000 * (1 + (0.07/2))^(2*1)
= $8000 * (1 + 0.035)^2
= $8000 * (1.035)^2
= $8000 * 1.0711225
= $8,568.98 (approximately)
Therefore, assuming Goran makes no payments, he would owe approximately $8,568.98 at the end of the year.