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

$1018.01

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=
`(APR)/(12)` %=
`(6.75)/(12)`%

⇒ Time Period for the loan to be repaid in months=
`7*12`

= 84 months

Annuity PV factor =
`(1-(1+r)^(-t) )/(r)` =
`(1-(1+(6.75)/(1200) )^(-84) )/((6.75)/(1200)) = 66.7968`

Principle=
`(\text{equal loan payment}) * (\text{Annuity PV factor})`

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

=
`(68000)/(66.7968)`

= $1018.01