# Effective yield

• Jan 4th 2007, 06:03 PM
xenophos
Effective yield
Okay here is the problem and this is all it tells you nothing more,

An antique was bought for \$3,000 and was sold 10 years later for \$6,000. Find the effective yield.
• Jan 4th 2007, 06:57 PM
OReilly
Quote:

Originally Posted by xenophos
Okay here is the problem and this is all it tells you nothing more,

An antique was bought for \$3,000 and was sold 10 years later for \$6,000. Find the effective yield.

What is "effective yield"?

Yield is profit (I think) and profit is \$3,000.
• Jan 4th 2007, 07:15 PM
xenophos
i do't think it's asking for profit, i looked up effective yield and got this but i can't figure out how to put it in the problem.

Effective Yield = ((1 + i/n) to the power of n) - 1
i = Nominal or stated interest rate
n = Number of compounding periods per year

Effective Yield -- A complete definition
• Jan 5th 2007, 02:22 AM
ticbol
Quote:

Originally Posted by xenophos
Okay here is the problem and this is all it tells you nothing more,

An antique was bought for \$3,000 and was sold 10 years later for \$6,000. Find the effective yield.

Effective yield, or effective rate, or true interest rate, is the equivalent simple interest rate per annum, without compounding.
In other words, if a principal is invested in compound interest and it yields to an amount A at the end of a time y, then an equivalent simple interest without compounding that will yield to the same amount A after the same time y is the effective rate or effective yield or true interest rate of that same investment.

That explanation does not even apply to your question here because the antique is not invested with an interest rate of any kind. The antique just appreciates in value with time. Still that is an investment. The effective yield then is the appreciation rate per annum as if the antique's value is earning/appreciating in simple interest without compounding.

A = P(1+r)^n
where
A = amount after n years
P = principal or initial amount at zero year
r = intrest rate per annum, in decimals
n = time in years

So,
6000 = 3000(1+r)^10
(1+r)^10 = 6000/3000 = 2
(1+r) = 2^(1/10) = 1.071773
r = 1.071773 -1 = 0.071773 = 7.1773 percent per annum.

Therefore, the effective yield on the antique's value is 7.1773 percent per year.----answer.