Final answer:
To find the past and future values of a house with a given compound interest rate, we use the compound interest formula. By plugging in the principal value, the annual interest rate, the number of compounding periods, and the time frame, we can calculate the value of the house 3.7 years ago and 3.7 years from now.
Step-by-step explanation:
The student's question asks about the future and past values of a house given a specific compound interest rate. Using the compound interest formula, we can calculate both the past and future values of the house. The relevant formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.
To solve for part (a), we need to find the value 3.7 years ago:
- P = $450,000 (current value)
- r = 19.5% or 0.195 (annual interest rate)
- n = 12 (compounded monthly)
- t = -3.7 (since we're looking back in time)
Now, we plug these values into the formula:
A = 450,000(1 + 0.195/12)^(-12*3.7)
After calculating, we'll get the past value of the house.
For part (b), we want to find the value 3.7 years from now, so t will be positive. The formula remains the same otherwise:
A = 450,000(1 + 0.195/12)^(12*3.7)
After calculating, we will find the future value of the house.