Question

-Exponential and Logarithmic Functions- Juan plans to retire in 20 yr..

Answer 1

`\$92,592.59`

Step-by-step explanation

We want to find how much Juan needs to invest now to meet his target.

To do this, we have to apply the formula for the amount for a quarterly compounded interest:

`A=P(1+(r)/(4))^(4t)`

where 4 represents 4 quarters in a year

P = principal or initial amount invested

r = interest rate

A = amount after t years

t = number of years

Therefore, substituting the given values into the equation, we have that:

`\begin{gathered} 250000=P(1+((5)/(100))/(4))^(4\cdot20) \\ 250000=P(1+(5)/(400))^(80) \\ 250000=P(1+0.0125)^(80) \\ 250000=P(1.0125)^(80) \\ 250000=P\cdot2.70 \end{gathered}`

Solve for P by dividing both sides by 2.70:

`\begin{gathered} P=(250000)/(2.7) \\ P=\$92,592.59 \end{gathered}`

That is the amount that he needs to invest now.