How much money would need to be deposited into an account earning 5.75% interest compounded annually in order for the accumulated value at the end of 25 years to be $85,000?
I will assume you are using compound interest.
let the amount invested be x
x(1.0575)^25 = 85000
x = 85000/1.0575^25 = $21,009.20
To find out how much money would need to be deposited into an account earning 5.75% interest compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated value at the end of the investment period
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years of the investment period
In this case, we have:
A = $85,000
r = 5.75% (or 0.0575 as a decimal)
n = 1 (compounded annually)
t = 25 years
We need to find the value of P.
Substituting the given values into the formula, we have:
$85,000 = P(1 + 0.0575/1)^(1*25)
Simplifying the equation:
$85,000 = P(1.0575)^25
To solve for P, we need to isolate it. Divide both sides of the equation by (1.0575)^25:
P = $85,000 / (1.0575)^25
Using a calculator, we can evaluate the right side of the equation to find the value of P.