Question

Aniyah needs to borrow $8000. She can borrow the money at 6% simple interest for 5 yr or she can borrow at 4% with interest compounded continuously for 5 yr

How much total interest would aniyah pay at interest compounded continuously?

Answer 1

Aniyah would pay approximately $1771.20 in total compound interest on an $8000 loan at 4% interest compounded continuously for 5 years, using the formula A = Pe^(rt).

Step-by-step explanation:

To determine how much total interest Aniyah would pay with interest compounded continuously, we need to use the formula for continuous compounding, A = Pert, where A is the future value, P is the principal, r is the annual interest rate, and t is the time in years.

For Aniyah's loan of $8000 at 4% compounded continuously for 5 years:

• Principal (P) = $8000
• Annual interest rate (r) = 4% or 0.04
• Time (t) = 5 years

First, we convert the interest rate from a percentage to a decimal by dividing by 100: 4% / 100 = 0.04.

Then we apply the formula:

A = 8000 * e(0.04 * 5) = 8000 * e0.2

We calculate e0.2 using a scientific calculator or an online tool, which gives us approximately 1.2214. So:

A = 8000 * 1.2214 ≈ $9771.20

The future value of the loan is approximately $9771.20. To find the total compound interest paid, we subtract the principal from this amount:

Total compound interest = Future value - Principal

= $9771.20 - $8000

≈ $1771.20

Aniyah would pay approximately $1771.20 in total compound interest over 5 years.