Barbara invested $12,300 at the Midtown Credit Union at 6% compounded monthly for 7 years. What is the effective rate of this investment?

Use compound interest formula:

monthly interest, i = 0.06/12=0.005
period, n = 7*12=84
Principal, P=1000 (say)
Future value
=P(1+i)^84
=1000*(1.005)^84
=1520.370
Effective rate (= average interest per year)
=((1520.370-1000)/7)/1000
=0.0743 p.a.

Sorry, Reiny is right.

What I calculated could be called "average rate of return".
Effective rate is calculated for one year only.
See:
http://www.jiskha.com/display.cgi?id=1397777653

Thank you very much!

To find the effective rate of this investment, we first need to understand what effective rate means.

Effective rate is the annual interest rate at which compound interest would yield the same accumulated value as the given interest rate compounded over the specified period.

In this case, the interest is compounded monthly for 7 years at a rate of 6%. So, the first step is to calculate the future value of the investment.

The formula for calculating the future value of an investment with compound interest is:

Future Value = Principal * (1 + (interest rate / number of compounding periods)) ^ (number of compounding periods * number of years)

Let's plug in the given values to calculate the future value of the investment:

Principal (P) = $12,300
Interest Rate (R) = 6% or 0.06 (in decimal form)
Number of compounding periods (n) = 12 (monthly)
Number of years (t) = 7

Future Value = $12,300 * (1 + (0.06 / 12))^(12 * 7)

Now we can calculate the future value of the investment by evaluating the expression.

Future Value = $12,300 * (1 + (0.005))^84

Calculating further:

Future Value = $12,300 * (1.005)^84

Future Value = $12,300 * 1.4859

Future Value = $18,265.17

So, the future value of the investment after 7 years is $18,265.17.

Now, to find the effective rate, we can use the formula:

Effective Rate = [(Future Value / Principal) ^ (1 / number of years)] - 1

Let's substitute the values:

Effective Rate = [(18,265.17 / 12,300) ^ (1 / 7)] - 1

Calculating further:

Effective Rate = (1.4859 ^ 0.1429) - 1

Effective Rate = 1.057 - 1

Effective Rate = 0.057

So, the effective rate of this investment is 5.7%.