Suppose $400 is invested for 4 years at a nominal yearly interest rate that is compounded monthly, further suppose it accumulates to 817.39 after 4 years. Find the annual nominal interest rate of the investment.

Answer 1

817.39/400 = 2.0435 = (1 + i)^4

Solve for i, the annual perecentage rate (not the nominal )

Take the square root of 2.043 twice.

1 + i = 1.1956

i = 19.56%

Now find the monthly-componded nominal annual rate I that yields that annual interest.

(1 + I/12)^12 = 1.1956
1 + I/12 = 1.0150
I = 0.180
I = 18%

This could have been done in one step, by considering 48 consecutive compounding intervals