Question

How much should you invest in a account paying 2.5%compound quarterly, in order to have $20,000 in 15 years?

Answer 1

Given:

Interest rate = 2.5% compounded quarterly

Final Amount = $20,000

Time = 15 years

Let's find the amount you should invest in the account.

Here, we are to find the principal amount.

Apply the formula:

`A=P(1+(r)/(n))^(nt)`

Where:

A is the final amount = $20,000

r is the rate = 2.5% = 0.025

compound frequency is n. Since it is compounded quarterly, n = 4

t is the time in years = 15 years.

Let's solve for P.

We have:

`\begin{gathered} 20000=P(1+(0.025)/(4))^(4*15) \\ \\ 20000=P(1+0.00625)^(60) \\ \\ 20000=P(1.00625)^(60) \end{gathered}`

Solving further:

`20000=P(1.45329)`

Divide both sides by 1.45329:

`\begin{gathered} (20000)/(1.45329)=(P(1.45329))/(1.45329) \\ \\ 13761.87=P \\ \\ P=13761.87 \end{gathered}`

Therefore, the amount that should be invested is $13,761.87

ANSWER:

$13,761.87