Answer:
$84,916.23
Step-by-step explanation:
To find the maximum price for a boat that Ryan's budget can afford, we can use the formula for calculating the principal loan amount (the initial amount borrowed) for a fixed-rate loan:
P = M / [ (r/12)x(1 - 1/(1+r/12)^(nx12)]
Where:
P is the principal loan amount (what we want to find).
M is the maximum monthly payment Ryan can afford ($900).
r is the annual interest rate (10% or 0.10).
n is the total number of years (8 years).
First, convert the annual interest rate to a monthly interest rate:
r=0.10/12=0.0083333
Now, plug these values into the formula:
P = 900 / [ (0.0083333 / 12)x(1- 1/(1 + 0.0083333/12)^(8x12) ]
Now, calculate P:
P≈$84,916.23
So, the maximum price for a boat that Ryan's budget can afford is approximately $84,916.23 when rounded to the nearest hundred dollars.