Question

Ryan wishes to purchase a new boat and can afford monthly payments of up to $500 per month. Finance is available, and the terms are that the loan lasts for 10 years and the annual interest rate is 13%. What is the maximum price for a boat that Ryan's budget can afford? Round your answer to the nearest hundred dollars.

Answer 1

First, we need to calculate the total number of payments Ryan will make over 10 years, which is 10 years x 12 months/year = 120 months.

Next, we can use the formula for the present value of an annuity to calculate the maximum price of the boat:

PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)

where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the values we have:

PMT = $500

r = 0.13

n = 12 (since the loan is monthly)

t = 10

PV = $500 x [1 - (1 + 0.13/12)^(-12x10)] / (0.13/12)

PV = $44,484.72

Therefore, the maximum price for a boat that Ryan's budget can afford, rounded to the nearest hundred dollars, is $44,500.