Question

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You are getting a personal loan for $10,000 a 7.2% APR that you are going to pay back over 7 years. What is the total paid?

Answer 1

Answer:

$12,760.13 (nearest cent)

Step-by-step explanation:

The formula to calculate the monthly payment for a loan with an APR is:

$\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}$

where:

• PMT = monthly payment
• P = loan amount
• i = interest rate per month (in decimal form)
• n = term of the loan (in months)

Given values:

• P = $10,000
• i = 7.2%/12 = 0.072/12 = 0.006
• n = 7 years = 7 × 12 = 84 months

Substitute the given values into the formula to find the monthly payment:

$\implies \sf PMT=\dfrac{10000 \cdot 0.006(1+0.006)^{84}}{(1+0.006)^{84}-1}$

$\implies \sf PMT = \dfrac{60(1.006)^{84}}{1.006^{84}-1}$

$\implies \sf PMT=151.9063658$

To find the total paid, simply multiply the found monthly payment (PMT) by the term of the loan (in months):

$\implies \sf Total\:paid=PMT \times 84$

$\implies \sf Total\:paid=151.9063658 \times 84$

$\implies \sf Total\:paid=12760.13473$

Therefore, the total paid is $12,760.13 (nearest cent).

Learn more about monthly payments here:

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