Question

Craig bought a new boat. He made a 18% down payment. He financed the rest through his bank for 4 years. His bank charged 4% per year compounded monthly and his monthly payments were $500. What was the original price of the boat?

Answer 1

Answer:

$27,005.62

Explanation:

Data provided in the question:

Down payment made = 18%

Monthly payment = $500

Interest rate, i = 4% per year compounded monthly

Time = 4 years

Now,

Present value of annuity = Monthly payment × $\left[ \frac{1-(1+i)^{-n}}{i} \right]$

n = number of periods

Here,

number of periods , n = 4 × 12 = 48 months

Interest rate per period, i = 0.04 ÷ 12 = 0.003333

on substituting the values

Present value of annuity = $500 × $\left[ \frac{1-(1+0.003333)^{-48}}{ 0.003333 } \right]$

or

Present value of annuity = $500 ×  $\left[ \frac{1 - 1.003333^{-48}}{ 0.003333} \right]$

or

Present value of annuity = $500 × $\left[ \frac{1 - 0.852384}{ 0.003333} \right]$

or

Present value of annuity = $500 × 44.289229

or

Present value of annuity = $22,144.61

also,

Present value of annuity is (100% - Down payment) i.e (100% - 18%) 82% of the original price

Therefore,

Original price of the boat =  $22,144.61 ÷ 82%

= $22,144.61 ÷ 0.82

= $27,005.62