Question

Sally Seair buys a sailboat. The price, including tax, is $5,275.00. She finances the boat over 36 months after making a $500 down payment. The true annual interest rate is 15%. What are Sally's monthly payments (principal plus interest)?

Answer 1

5,275−500
=4,775
C
(0.15×4,775×37)÷(2×12)
=1,104.21875
Total payments
1,104.22+4,775
=5,879.22
Monthly payment
5,879.22÷36
=163.31

Answer 2

Sally's monthly payments is $165.53

Solution-

The cost of the sailboat = $5,275

Down payment amount = $500

The amount she financed = 5275-500 = $4775

We know that,

`\text{PV of annuity}=P[(1-(1+r)^(-n))/(r)]`

Here,

Present Value of annuity = $4775

r = rate of interest = 15% annual =
`(15)/(12)\%` monthly = 1.25% monthly

n = time period = 36

Putting the values,

`\Rightarrow 4775=P[(1-(1+0.0125)^(-36))/(0.0125)]`

`\Rightarrow 4775=P[(1-(1.0125)^(-36))/(0.0125)]`

`\Rightarrow P=(4775)/((1-(1.0125)^(-36))/(0.0125))`

`\Rightarrow P=\$165.53`

Therefore, Sally's monthly payments is $165.53