Question

You borrowed $10,400 for four years at 12.7% and the interest is compounded semi annually. what is the total you pay back?

Answer 1

To calculate the total repayment of a $10,400 loan at 12.7% interest compounded semi-annually for four years, use the compound interest formula A = P(1 + r/n)^(nt) to find A, which comes out to approximately $17,869.97.

Step-by-step explanation:

To calculate the total amount to be paid back on a loan of $10,400 with a compound interest rate of 12.7% compounded semi-annually for four years, we need to use the formula for compound interest A = P(1 + r/n)^(nt), where:

In this case,

• P = $10,400
• r = 12.7% or 0.127 (as a decimal)
• n = 2 (since interest is compounded semi-annually)
• t = 4 years

First, let's convert the annual interest rate to the rate per period by dividing by the number of periods per year:

r/n = 0.127/2 = 0.0635

Now we calculate the compound interest using the given formula:

A = 10400(1 + 0.0635)^(2*4)

A = 10400(1 + 0.0635)^8

A = 10400(1.0635)^8

A = 10400 * 1.718189

A = $17869.9664

The total amount that needs to be paid back is approximately $17,869.97.

Answer 2

A= 10,400(1 +(.127/2))^8
A=$17,018.97