Question

Assume you just bought a new boat and now have a boat loan to repay. The amount of the principal is $68,000, the loan is at 6.75% APR, and the monthly payments are spread out over 7 years. What is the loan payment? Use a calculator to determine your answer.
a) $1,225.36
b) $1,081.01
c) $809.52
d) $1,206.58

Answer 1

Answer:

$1018.01

Step-by-step explanation:

Given

Principle= $68,000

APR(Annual Percentage Rate)= 6.75%

Time=7 years

As loan is repaid with equal monthly payments,

lets compound the loan monthly

⇒ Rate of interest for compounding monthly= $\frac{APR}{12}$ %=$\frac{6.75}{12}$%

⇒ Time Period for the loan to be repaid in months= $7\times12$

                                                                                    = 84 months

Annuity PV factor = $\frac{1-(1+r)^{-t} }{r}$ = $\frac{1-(1+\frac{6.75}{1200} )^{-84} }{\frac{6.75}{1200}} = 66.7968$

Principle= $(\text{equal loan payment}) \times (\text{Annuity PV factor})$

⇒ Loan payment =$\frac{\text{Principle}}{\text{Annuity PV factor}}$

                             =$\frac{68000}{66.7968}$

                             = $1018.01