Question

jessie needs to borroe 12,000 from northwestern bank. they offeted her a 5 year loan with an apr of 4.98%. how much will she pay interest over the life of the loan?

Answer 1

$1580.69

Explanation:

Monthly Payment Formula

`\sf PMT=(Pi\left(1+i\right)^n)/(\left(1+i\right)^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:

• P = $12,000
• i = 0.0498/12 = 0.00415
• n = 5 years = 60 months

Substitute the values into the formula to calculate the monthly payment:

`\implies \sf PMT=(12000(0.00415)\left(1+0.00415\right)^(60))/(\left(1+0.00415\right)^(60)-1)`

`\implies \sf PMT=(49.8\left(1.00415\right)^(60))/(\left(1.00415\right)^(60)-1)`

`\implies \sf PMT=(63.84764727)/(0.2820812705)`

`\implies \sf PMT=226.3448656`

Therefore, the total payments over the life of the loan is the monthly payment multiplied by the total number of months:

`\implies \sf 226.3448656 * 60=\$13580.69`

To calculate how much interest Jessie pays over the life of the loan, subtract the original loan amount from the total payments amount:

`\implies 13580.69-12000=\$1580.69`

Therefore, the interest Jessie will pay over the life of the loan is $1580.69.

Answer 2

• 1580.40

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Given

• Loan amount P = 12000,
• Rate r = 4.98% = 0.0498,
• Time t = 5 years,
• Number of compounds n = 12.

Find the monthly payment

• 
  `M=(P(r/n)(1+r/n)^(nt))/((1+r/n)^(nt)-1)`

• 
  `M=(12000(0.0498/12)(1+0.0498/12)^(12*5))/((1+0.0498/12)^(12*5)-1) =226.34`

Find the total amount paid

• 226.34*60 = 13580.40

Find the amount of interest

• 13580.40 - 12000 = 1580.40