question 9, 4.b.85\nwork: the power of compounding\nhow much must be deposited today into the following…

question 9, 4.b.85\nwork: the power of compounding\nhow 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%\n$34672.75 should be deposited today (do not round until the final answer. then round to the nearest cent as needed.)

question 9, 4.b.85\nwork: the power of compounding\nhow 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%\n$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:

$34672.75$