Question

Olivia wants $1500.00 in 2 years at an interest rate of 4 %/a compounded semi-annually. How much should she invest?

Answer 1

Given -

Final Amount = $1500.00

Time Period = 2 years

Rate of interest = 4% compounded semi-annually.

To Find -

How much should she invest (Principle Amount)=?

Step-by-Step Explanation -

We know the formula for the compound interest

`A\text{ = P\lparen1 + }(r)/(n)\text{\rparen}^(nt)`

Where,

n = 2

As it is semi-annually

Now, putting the values in the formula

`\begin{gathered} 1500.00\text{ = P\lparen1+ }(.04)/(2)\text{\rparen}^(2*2) \\ \\ 1500.00\text{ =P\lparen1 + .02\rparen}^4 \\ \\ 1500.00\text{ = P\lparen1.02\rparen}^4 \\ \\ P\text{ = }(1500.00)/(1.08) \\ \\ P\text{ = 1388.88} \end{gathered}`

Final Answer -

Principle Amount = $1388.88