MATH SOLVE

3 months ago

Q:
# 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) $1,225.36b) $1,081.01c) $809.52d) $1,206.58

Accepted Solution

A:

Answer:$1018.01Step-by-step explanation:GivenPrinciple= $68,000APR(Annual Percentage Rate)= 6.75%Time=7 yearsAs loan is repaid with equal monthly payments, lets compound the loan monthly⇒ Rate of interest for compounding monthly= [tex]\frac{APR}{12}[/tex] %=[tex]\frac{6.75}{12}[/tex]%⇒ Time Period for the loan to be repaid in months= [tex]7\times12[/tex] = 84 monthsAnnuity PV factor = [tex]\frac{1-(1+r)^{-t} }{r}[/tex] = [tex]\frac{1-(1+\frac{6.75}{1200} )^{-84} }{\frac{6.75}{1200}} = 66.7968[/tex]Principle= [tex](\text{equal loan payment}) \times (\text{Annuity PV factor})[/tex]⇒ Loan payment =[tex]\frac{\text{Principle}}{\text{Annuity PV factor}}[/tex] =[tex]\frac{68000}{66.7968}[/tex] = $1018.01