Question

A sailboat cost 31,567. You pay 20% down and amortize the rest with the equal monthly payments over 14- year period. If you must pay 6.6 compounded monthly , what is your monthly payment. How much interest will you pay

Answer 1

The annuity formula is given to be:

`PV=PMT\cdot(1-(1+i)^(-n))/(i)`

where

PV = Present Value

PMT = Periodic Payment

i = Interest Rate

n = Number of Periods

If one is to pay 20% down, the loan percentage will be:

`1-0.2=0.8\%`

Therefore, the loan amount will be:

`\Rightarrow0.8*31567=25253.6`

The interest rate is 6.6%. The monthly rate will therefore be:

`\Rightarrow(6.6)/(100*12)=0.0055`

The number of periods over 14 years is gotten to be:

`\Rightarrow14*12=168`

Therefore, we have the following parameters to work with:

`\begin{gathered} PV=25253.6 \\ i=0.0055 \\ n=168 \end{gathered}`

To calculate the PMT, we can rewrite the annuity formula to give:

`PMT=(PV\cdot i)/(1-(1+i)^(-n))`

Therefore, we can solve to be:

`\begin{gathered} PMT=(25253.6*0.0055)/(1-(1+0.0055)^(-168)) \\ PMT=230.70 \end{gathered}`

Therefore, the monthly payment is 230.70.

The amount paid is given to be:

`\Rightarrow230.70*168=38757.6`

Therefore, the interest paid is:

`\Rightarrow38757.6-25253.6=13504`

Therefore, the interest paid is 13,504.