Barbara invested $12,300 at the Midtown Credit Union at 6% compounded monthly for 7 years.
What is the effect rate of this investment?
If what you want is the effective annual rate, all we need is the 6% per annum compounded monthly
let the annual rate be i
then 1+i = (1 + .06/12)^12
1+i = 1.005^12 = 1.0616778..
i = .0616778
the effective annual rate correct to 3 decimals is
6.168 %
check:
amount of 12300 at 6% compounded monthly for 7 years
= 12300(1.005)^84 = $18,700.54
amount of 12300 at 6.616778% for 7 years
= 12,300(1.0616778)^7 = $18,700.54
the same!
To calculate the effective rate of an investment, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Barbara invested $12,300 at an annual interest rate of 6%, compounded monthly for 7 years. Let's calculate the future value (A) using the formula:
P = $12,300
r = 6% or 0.06 (as a decimal)
n = 12 (monthly compounding)
t = 7
A = $12,300(1 + 0.06/12)^(12*7)
Now, we can calculate the future value (A):
A = $12,300(1 + 0.005)^(84)
A ≈ $19,849.12
The future value of the investment after 7 years is approximately $19,849.12.
To find the effective rate of the investment, we can use the following formula:
Effective Rate = ((A / P)^(1/n*t) - 1) * n
Plug in the values we calculated:
Effective Rate = (($19,849.12 / $12,300)^(1/(12*7)) - 1) * 12
Effective Rate ≈ 0.0538 or 5.38%
Therefore, the effective rate of Barbara's investment at the Midtown Credit Union is approximately 5.38%.