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Doss [256]
3 years ago
6

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

Mathematics
2 answers:
stich3 [128]3 years ago
8 0

The monthly payment is $ 1892.392

<em><u>Solution:</u></em>

<em><u>The formula for compound interest, including principal sum, is:</u></em>

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 )

<em><u>Substituting the values we get,</u></em>

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

<em><u>What will her monthly  payment be?</u></em>

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

Thus monthly payment is $ 1892.392

lisabon 2012 [21]3 years ago
7 0

Her monthly  payment will be $171.045

<u>Step-by-step explanation</u>:

  • Principal, P = $12,500
  • Rate, r = 12% = 0.12
  • Time period, t = 5 years.
  • Number of times interest applied, n = compounded  monthly.
  • n = 5\times12 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\times1.821

⇒ $22,762.5

Interest = Amount - Principal

⇒ 22,762.5 - 12,500

⇒ $10,262.5

Monthly payment = 10,262.5 / 60 months

⇒ $171.045

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