Question

How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.I want answer and explanation.

Answer 1

The rule of the simple interest is

`\begin{gathered} I=PRT \\ A=P+I \end{gathered}`

I is the amount of interest

P is the initial amount

R is the interest rate in decimal

T is the time

We need to find the initial amount if the new amount is $20,000, the interest rate is 5% for 4 years, then

A = 20000

R = 5/100 = 0.05

T = 4

Substitute them in the rules above

`\begin{gathered} I=P(0.05)(4) \\ I=0.2P \\ 20000=P+0.2P \\ 20000=1.2P \\ (20000)/(1.2)=(1.2P)/(1.2) \\ 16666.67=P \end{gathered}`

You need to deposit $16,666.67

The rule of the compounded interest

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

A is the new amount

P is the initial amount

r is the interest rate in decimal

t is the time

A = 20000

r = 0.05

t = 4

Substitute them in the rule above

`\begin{gathered} 20000=P(1+0.05)^4 \\ 20000=P(1.05)^4 \\ (20000)/((1.05)^4)=(P(1.05)^4)/((1.05)^4) \\ 16454.05=P \end{gathered}`

You need to deposit $16,454.05