Compound interest

Question

The present value P of A dollars t years from now earning annual interest r compounded n times per year is P=A (1+r/n)^-nt in this context,  A is called the future value.  Find the interest rate (to two decimals) necessary for a present value of $3200 to grow to a future value of $4,177 if interest is compounded monthly for 4 years. 

Answer 1

P = A(1 + r/n)^nt

4177 = 3200(1 + r/12)^(12)(4)

1.3053125 = (1 + r/12)⁴⁸        Raise both sides to the 1/48 power.

1.00556632 = 1 + r/12       Subtract 1 from both sides.

.00556632 = r/12              Multiply both sides by 12.  

.0667958 = r

r ≈ 6.68%