TheCrimsonFox
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You purchase a car using a $20,000 loan with a 5% simple interest rate.
(a) Suppose you pay the loan off after 4 years. How much interest do you pay on your loan? Show your work.
(b) Suppose you pay the loan off after 2 years. How much interest do you save by paying the loan off sooner? Show your work.

Respuesta :

Simple Interest = Cost Price + (Interest Percentage of Cost Price × number of years or months you are paying off)

a) SI = $20 000 + (5% of $20 000 × 4)
SI = $20 000 + ($1000 × 4)
SI = $20 000 + $4000 = $24 000

b) SI = $20 000 + (5% of $20 000 × 2)
SI = $20 000 + ($1000 × 2)
SI = $20 000 + $2000 = $22 000

$24 000 - $22 000 = $2000 that you save!

a) Interest paid after 4years =$4000 .

b) Interest paid after 2years = $2000.

    Interest saved by paying loan sooner = $2000.

What is simple interest?

" Simple interest is defined as method of calculating the interest on a principal amount with fixed rate of interest for time period."

Formula used

Simple Interest = ( P × R × T ) / 100

P = Principal

R = Rate of interest

T = Time period

According to the question,

Given,

Principal = $20,000

Rate of interest = 5%

a) Time period = 4years

Substitute the value in the formula we get,

Simple Interest = (20,000 × 5 × 4 ) / 100

                         = $4,000                                       _____(1)

b) Time period = 2years

Substitute the value in the formula we get,

Simple Interest = (20,000 × 5 × 2 ) / 100

                         = $2,000                                       _____(2)

From (1) and (2) we get

Interest saved by paying loan sooner  = $4000 - $2000

                                                                = $2000

Hence, a) Interest paid after 4years =$4000 ,  b) Interest paid after 2years = $2000. Interest saved by paying loan sooner= $2000.

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