Final answer:
To calculate the amount borrowed, use the formula for compound interest and solve for the principal. Plug in the values into the formula and divide the total amount borrowed by the future value factor.
Step-by-step explanation:
To calculate the amount borrowed, we need to use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where A is the total amount, P is the principal (amount borrowed), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal (amount borrowed) is unknown and that's what we need to find. The annual interest rate is 12% (or 0.12 as a decimal). The loan matures in 5 years, so t = 5. The interest is compounded monthly, so n = 12.
Plugging in the values into the formula, we have:
X = P(1 + 0.12/12)^(12*5)
Simplifying further:
X = P(1.01)^60
Since we know X is the total amount borrowed, we can rewrite the equation as:
X = P(1.01)^60 = P * future value factor
To find P, divide X by the future value factor:
P = X / future value factor