Answer to Question #65537 in Financial Math for Rammeya

Question

What is the effective annual rate of interest if ​$900.00900.00 grows to ​$1400.001400.00 in years compounded quarterly​? round 4 decimal places as needed.

Answer 1

If ​$900.00 grows to ​$1400.00 in years compounded quarterly​, then:
1400 = 900*(1 + i/4)^4,
(1 + i/4)^4 = 14/9,
1 + i/4 = 1.1168,
i = 0.4672 or 46.72%.
Effective rate of​ interest can be calculated using formula: r = (1 + i/n)^n - 1, where i - nominal interest rate, n - number of compounding periods.
r = (1 + 0.4672/4)^4 - 1 = 0.5556 or 55.56%.