How long did it take for an investment of $27,500 to grow to $31,000 at 1.59% compounded semi-annually?
To find out how long it takes for an investment of $27,500 to grow to $31,000 at 1.59% compounded semi-annually, we can use the formula for compound interest which is given as;
A = P(1 + r/n)^(n*t)
Where;
A = amount of investment after t years,
P = principal investment,
r = annual interest rate,
n = number of times interest is compounded per year,
t = time in years
First, let us determine the values of the given variables.
P = $27,500, A = $31,000, r = 1.59%, n = 2 (compounded semi-annually), T = number of years we want to find out
Now, we will substitute the given values into the formula and solve for t as follows;
A = P(1 + r/n)^(n*t)
$31,000 = $27,500(1 + 1.59%/2)^(2*t)
Dividing both sides by $27,500 gives;
1.12727 = (1 + 0.00795)^2t
Using logarithms, we can solve for t as follows;
t = log(1.12727) / (2 * log(1.00795))
t = 3.92 years
Therefore, the investment took approximately 3 years and 11 months to grow to $31,000 at 1.59% compounded semi-annually, rounded to two decimal places.
Understanding Compound Interest:
Compound Interest Calculation:
Compound interest is calculated by adding the interest earned to the principal amount, and then calculating the interest for the next period. This means that the interest for each period is calculated on the initial principal amount plus the interest from previous periods.
Formula for Compound Interest:
The formula for compound interest is given by:
A = P(1 + r/n)^(n*t)
Where:
- A is the amount of investment after t years
- P is the principal investment
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the time in years
Calculating Time Taken for Investment Growth:
In the given scenario, an investment of $27,500 grew to $31,000 at an annual interest rate of 1.59% compounded semi-annually. By substituting the values into the compound interest formula and solving for t, we found that it took approximately 3 years and 11 months for the investment to grow to $31,000.
This calculation demonstrates the importance of understanding compound interest and how it affects the growth of investments over time. By utilizing the compound interest formula, investors can make informed decisions regarding their investments and plan for future financial goals effectively.