how much must be deposited today into the following account in order to have a $140,000 college fund in 18…

how much must be deposited today into the following account in order to have a $140,000 college fund in 18 years? assume no additional deposits are made. an account with annual compounding and an apr of 7.9% $34672.75 should be deposited today (do not round until the final answer. then round to the nearest cent as needed.)

how much must be deposited today into the following account in order to have a $140,000 college fund in 18 years? assume no additional deposits are made. an account with annual compounding and an apr of 7.9% $34672.75 should be deposited today (do not round until the final answer. then round to the nearest cent as needed.)

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula for present value $PV$ when compounded annually is $PV=\frac{FV}{(1 + r)^t}$, where $FV$ is the future value, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years.

Step2: Identify the values

We are given that $FV = 140000$, $r=0.079$ (since $7.9%=0.079$), and $t = 18$.

Step3: Substitute values into the formula

$PV=\frac{140000}{(1 + 0.079)^{18}}$. First, calculate $(1 + 0.079)^{18}$. Using a calculator, $(1.079)^{18}\approx4.0376$. Then, $PV=\frac{140000}{4.0376}\approx34672.75$.

Answer:

$34672.75$