Question

Brenda took out a personal loan for $12,500 at an interest rate of 12% compounded

Answer 1

The monthly payment is $ 1892.392

Solution:

The formula for compound interest, including principal sum, is:

$A = p(1 + \frac{r}{n})^{nt}$

Where,

A = the future value of the investment

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

From given,

p = 12500

t = 5 years

$r = 12 \% = \frac{12}{100} = 0.12$

n = 12 ( compounded mothly )

Substituting the values we get,

$A = 12500( 1 + \frac{0.12}{12})^{ 12 \times 5}\\\\A = 12500 ( 1 + 0.01)^{60}\\\\A = 12500 \times 1.8166\\\\A = 22708.7087$

What will her monthly  payment be?

$Monthly\ payment = \frac{22708.7087}{12} = 1892.392$

Thus monthly payment is $ 1892.392

Answer 2

Her monthly  payment will be $171.045

Step-by-step explanation:

• Principal, P = $12,500
• Rate, r = 12% = 0.12
• Time period, t = 5 years.
• Number of times interest applied, n = compounded  monthly.
• n = 5$\times$12 months = 60.

Amount = P(1+r/n)^nt

⇒ 12,500(1+0.12/60)^300

⇒ 12500(60.12/60)^300

⇒ 12500(1.002)^300

⇒ 12500$\times$1.821

⇒ $22,762.5

Interest = Amount - Principal

⇒ 22,762.5 - 12,500

⇒ $10,262.5

Monthly payment = 10,262.5 / 60 months

⇒ $171.045