Question

A sailboat costs $26,232. You pay 10% down and amortize the rest with equal monthly payments over a 8-year period. If you must pay 7.5% compounded monthly.what is your monthly payment? How much interest will you pay?Monthly payments: $(Round to two decimal places.)Interest: $(Round to two decimal places.)

Answer 1

Step 1- Write out the Present Value of Annuity formula:

`PV=P*(1-(1+(r)/(n))^(-t* n))/((r)/(n))`

Where

`\begin{gathered} PV=\text{ the present value} \\ P=\text{ the periodic payment} \\ n=\text{ the number of payments in a year} \\ r=\text{ annual interest rate} \end{gathered}`

Step 2- Write out the given values and substitute them into the formula:

`\begin{gathered} PV=\$26232(1-0.1)=\$26232*0.9=\$23608.80 \\ n=12 \\ r=0.075 \end{gathered}`

Substituting the values into the formula, we have:

`23608.80=P*(1-(1+(0.075)/(12))^(-8*12))/((0.075)/(12))`

Therefore,

`23608.80=72.0260P`

Dividing both sides by 72.0260, we have:

`P=\$327.78`

Hence, the monthly payment is $327.78.

The total amount T paid is given by:

`T=\$327.78*8*12=\$31466.88`

Hence, the interest I is given by:

`I=31466.88-23608.80=\$7858.08`

Therefore, the monthly payment is $327.78 and the interest paid is $7858.08