Question

Brad has purchased a new boat for $20,000. He paid $3,000 as down payment and he paid the balance by a loan from his hometown bank. The loan is to be paid on a monthly basis for two years charging 6 percent interest. How much are the monthly payments? How much interest will he pay in his first monthly payment?

Answer 1

• Monthly payment = $753.45
• Interest in first month = $85

First remove the amount paid as down payment:

= 20,000 - 3,000

= $17,000

The amount to be paid monthly is a constant amount which would make it an Annuity.

The $17,000 is the present value of this Annuity so the formula for present value of annuity can be used to find the annuity.

The payment is monthly so the rate and number of periods needs to be converted:

Rate = 6%/12 = 0.5%

Period = 2 x 12 = 24 months

Annuity is:

Present value of Annuity = Annuity x ( 1 - (1 + rate) ^- number of periods) / rate

17,000 = A x ( 1 - ( 1 + 0.5%)⁻²⁴) / 0.5%

17,000 = A x 22.5628662

A = 17,000 / 22.5628662

A = $753.45

The interest in the first month is:

= Interest rate x Amount borrowed

= 0.5% x 17,000

= $85

In conclusion, the monthly payments will be $753.45 and the interest in the first month will be $85.

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