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

Answer:

Difference in total payback = $5734.64

Step-by-step explanation:

Formula for the simple interest payout,

Interest = $\frac{P\times r\times t}{100}$

P = Principal amount of loan

r = rate of interest (Annually)

t = Duration for the payment

Interest = $\frac{18000\times 14.5\times 5}{100}$

             = $13050

Total payable amount = 18000 + 13050

                                     = $31050

Formula for the amount payable with compound interest,

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

Here, t = Duration of investment

r = rate of interest (Annual)

n = Number of compounding per year

Payable amount = $18000(1+\frac{0.089}{1})^4$

                           = 18000(1.089)⁴

                           = $25315.36

Difference in total payback = $31050 - $25315.36

                                              = $5734.64