Question

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

monthly. She made arrangements to pay the loan off in 5 years. What will her monthly
payment be?

Answer 1

Her monthly payment will be $171.045

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
  `*`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
`*`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

Answer 2

The monthly payment is $ 1892.392

Solution:

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

`A = p(1 + (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 \% = (12)/(100) = 0.12`

n = 12 ( compounded mothly )

Substituting the values we get,

`A = 12500( 1 + (0.12)/(12))^( 12 * 5)\\\\A = 12500 ( 1 + 0.01)^(60)\\\\A = 12500 * 1.8166\\\\A = 22708.7087`

What will her monthly payment be?

`Monthly\ payment = (22708.7087)/(12) = 1892.392`

Thus monthly payment is $ 1892.392