Question

Lucas is borrowing money to purchase a vehicle. A car dealership will loan Lucas $18,000 with a simple interest rate of 14.5% applied annually, and a 5-year payout plan. The bank will loan Lucas $18,000 with a compound interest rate of 8.9% applied annually and a 4-year payout plan. What is the difference in the total payback amounts?

Answer 1

If Lucas takes the 5-year payment plan he will end up paying $31,050. If Lucas takes the 4-year payment plan he will end up playing $24,408. Hope it helps.

Answer 2

Difference in total payback = $5734.64

Explanation:

Formula for the simple interest payout,

Interest =
`(P* r* t)/(100)`

P = Principal amount of loan

r = rate of interest (Annually)

t = Duration for the payment

Interest =
`(18000* 14.5* 5)/(100)`

= $13050

Total payable amount = 18000 + 13050

= $31050

Formula for the amount payable with compound interest,

Final amount =
`\text{Initial amount}(1+(r)/(n))^t`

Here, t = Duration of investment

r = rate of interest (Annual)

n = Number of compounding per year

Payable amount =
`18000(1+(0.089)/(1))^4`

= 18000(1.089)⁴

= $25315.36

Difference in total payback = $31050 - $25315.36

= $5734.64