Question

Dave wants to borrow $22,000 from First Finance Bank. The bank
will give him a 15-year loan at an interest rate of 4.85%. How much
Will he pay the bank in interest over the life of the loan? Round to
the nearest hundred dollars.

Answer 1

• Principle=P=22000
• R=4.85%
• T=15yr

Interest be I

$\\ \rm\rightarrowtail I=\dfrac{PRT}{100}$

$\\ \rm\rightarrowtail I=\dfrac{22000(4.85)(15)}{100}$

$\\ \rm\rightarrowtail I=680.41$

Answer 2

Answer:

$9,000 (to the nearest hundred dollars)

Step-by-step explanation:

Loans from banks are usually amortizing loans, which is a type of loan that requires regular monthly payments.

To calculate the regular monthly payment:

$\sf PMT=\dfrac{P\left(\dfrac{r}{n}\right)}{1-\left(1+\dfrac{r}{n}\right)^{-nt}}$

where:

• PMT = regular monthly payment
• P = principal
• r = interest rate in decimal form
• n = number of payments per year
• t = length of loan (in years)

Given:

• P = 22000
• r = 0.0485
• n = 12
• t = 15

$\sf PMT=\dfrac{2000\left(\dfrac{0.0485}{12}\right)}{1-\left(1+\dfrac{0.0485}{12}\right)^{-12 \cdot 15}}=172.2604115...$

Number of months in 15 years = 15 × 12 = 180

⇒ Total payment over the term of the loan = 180 × 172.2604115...

                                                                       = 31006.87406...

Total interest = total payment - principal

                      = 31006.87406... - 22000

                      = 9006.87406...

                      = $9,000 (to the nearest hundred dollars)