Adrianna want to set aside some money for a vacation in 3 years. How much does Adrianna need to set aside today in order to have $8600 in 3 years if it is invested at 5% compounded annually. I am so confused!! Thanks for all your help!!
1.05^3 = 1.157625
1.157625 * x = 8600
x = 7429.00
P = Po*(1+r)^n = $8600
r = 5%/100% = 0.05
n = 1comp./yr. * 3yrs. = 3 Compounding
periods.
Po*(1.05)^3 = 8600
Po = 8600/1.05^3 = $7429.00 To be set
aside today.
No problem! I'll be happy to help you understand how to calculate the amount Adrianna needs to set aside today to have $8600 in 3 years, given an annual interest rate of 5% compounded annually.
To calculate this, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (in this case, $8600)
P = the principal amount (the amount Adrianna needs to set aside today)
r = the annual interest rate (5%, which is 0.05 expressed as a decimal)
n = the number of times interest is compounded per year (in this case, once annually)
t = the number of years (3 years)
Using the formula, we can rearrange it to solve for P:
P = A / (1 + r/n)^(nt)
Now, let's plug in the values:
P = 8600 / (1 + 0.05/1)^(1*3)
First, let's simplify the denominator:
1 + 0.05/1 = 1.05
Next, let's simplify the exponent:
1 * 3 = 3
Now, let's calculate the expression inside the parentheses:
(1.05)^3 = 1.157625
Finally, let's substitute the values into the equation:
P = 8600 / 1.157625
Using a calculator, we find that P ≈ $7443.93 (rounded to two decimal places)
Therefore, Adrianna needs to set aside approximately $7443.93 today in order to have $8600 in 3 years, given an annual interest rate of 5% compounded annually.