Question

Mary is looking to purchase a sailboat . She has her eye on a 39 foot Benneteau. The price with options is $428,000 including tax. She has $60,000 for a down payment and is looking to finance the rest on a monthly basis. She wants her to know her monthly payments if she gets a loan at an annual percentage rate (APR) of 6% and pays off the loan in 15 years. To keep the payments low she has agreed to a balloon payment at the end of loan of $100,000.

Answer 1

Different assumptions can be taken. I will take this assumption: "After Mary pays downpayment, she pays a certain amount (which we have to find out), for 14 years every month. On the 15th year, she pays $100,000, and the loan will be paid off completely with that."

[Note: Other assumptions can be that she pays a certain sum for 15 years every month, in addition to $100,000 at the end of the 15th year, etc. If you have any assumption other than the one I took (which I typed in bold above), please state, and I will work out accordingly].

So,

• Interest Rate per annum: 6%
• Interest Rate per month: 0.50%
• Cost: $428,000
• Downpayment: $60,000
• Balance: $368,000
• Balloon Payment at 15th year: $100,000
  - From this, we can know that the present value of balloon payment = $41,726.51, being $100,000 / 1.06¹⁵
• Therefore, the amount of loan for our calculation purposes can be taken as $326,273.49, being $368,000 - $41,726.51.
• Now, we need to find equal monthly payments that will be made for 14 years (168 monthly instalments) at 0.50% to repay $326,273.49.
  That will be 2,875.24, being $326,273.49 / [Present value annuity of $1 for 168 periods at 0.50%], that is, $326,273.49 / 113.4770. You can use Excel formula =PV(0.50%,168,-1) and it will yield result as 113.4770. You can use normal calculator to find it too. There will be rounding differences at the end when we take annuity as exactly 113.4770 as the actual value will be 113.47699.... However if we take the exact value using excel, such difference will not arise.

So the monthly amount will be $2,875.24 [there will be rounding differences]. Note: This is worked out using the assumption I laid out in the beginning. It can be a very different amount if different assumptions are taken. Give me your assumptions and I will work out that way too