how much money would need to be deposited into an account earning 5.75% interest compounded annually in…
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?\na. $75,425.52\nb. $59,130.43\nc. $21,009.20\nd. $20,258.70\nplease select the best answer from the choices provided
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the accumulated value, $P$ is the principal (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We need to solve for $P$, so we can rewrite the formula as $P=\frac{A}{(1 + r)^t}$.
Step2: Convert the interest rate to decimal
The annual interest rate $r = 5.75%=0.0575$, $A = 85000$, and $t = 25$.
Step3: Substitute values into the formula
$P=\frac{85000}{(1 + 0.0575)^{25}}$. First, calculate $(1 + 0.0575)^{25}$. Using a calculator, $(1.0575)^{25}\approx4.0724$. Then, $P=\frac{85000}{4.0724}\approx20872.65$. The closest value to this result among the options is $20258.70$.
Answer:
D. $$20,258.70$