Question

If a person borrows $2500.00 and, after 9 months, pays off the loan in the amount of $2603.13, what per annum rate of interest was charged?

Answer 1

Answer:

The annual interest rate was of 5.5%.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.

After t years, the total amount of money is:

$T = E + P$.

In this problem:

Borrows 2500, so $P = 2500$

Pays off the loan at $2603.13, so $T = 2603.13$

This means that

$T = E + P$.

$2603.13 = E + 2500$

$E = 103.13$

We also have

9 months. An year has 12 months, so $t = \frac{9}{12} = 0.75$

We have to find I.

$E = P*I*t$

$103.13 = 2500*I*0.75$

$I = \frac{103.13}{2500*0.75}$

$I = 0.055$

The annual interest rate was of 5.5%.