How much would you need to invest to get $30,000 in 10 years for an account offering 2.54%
interest?
P(1.0254)^10 = 3000
solve for P
What is the compounding frequency?, Quarterly ? annually ?
To determine the amount you would need to invest in order to get $30,000 in 10 years with an interest rate of 2.54%, you can utilize the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment (in this case, $30,000)
- P is the principal amount (the initial investment we want to find)
- r is the interest rate (2.54% expressed as a decimal: 0.0254)
- n is the number of times interest is compounded per year (assuming annual compounding)
- t is the number of years (10)
Now, let's plug in the values into the formula and solve for P:
$30,000 = P(1 + 0.0254/1)^(1*10)
Simplifying the equation:
$30,000 = P(1 + 0.0254)^(10)
Next, we can divide both sides by (1 + 0.0254)^10 to isolate P:
P = $30,000 / (1 + 0.0254)^10
Calculating this using a calculator or a spreadsheet software, you will find that P is approximately $23,581.18.
Therefore, you would need to invest around $23,581.18 in an account offering a 2.54% interest rate to accumulate $30,000 in 10 years.