The future value of the above investment (compounded quarterly) is $2,027.39 while the future value of the same investment compounded annually is $1,981.37. Hence it is better to compound at a quarterly rate.
<h3>What is compound interest?</h3>
Compound interest is the interest on savings computed on both the initial principle and the interest earned over time.
To compare an investment compounded quarterly to one compounded annually, we need to calculate the final amount of each investment after 11 years. We can use the formula for compound interest to do this.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
where:
- A is the final amount of the investment
- P is the principal of the investment
- r is the annual interest rate
- n is the number of times the interest is compounded per year
- t is the number of years the investment is held for
For the investment compounded annually, we can plug the values into the formula like this:
A = 1000(1 + 0.07/1)^(1*11) = 1000(1.07)^11
= $1981.37
For the investment compounded quarterly, we can plug the values into the formula like this:
A = 1000(1 + 0.07/4)^(4*11) = 1000(1.0175)^44
= $2027.39
In this case, the investment compounded quarterly has a higher final amount than the investment compounded annually. This is because the investment compounded quarterly compounds the interest more frequently, so the investment grows faster.
Learn more about compound interest:
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