Question

Use the formula for compound amount to find the compound amount:$20,000 at 5% compounded quarterly for 3/4 of a year

Answer 1

The formula we need to use is as follows:

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

Where:

A - Ajusted amount

P - Starting amount

r - Annual interest rate

n - How many times it is compounded per year

t - Time of the period in years

Since we want to find the compounded amount, that is, the adjusted A, the value given below, $20,000, is the starting amount, P.

Assuming the 5% is the annual interest, this is r.

Since the interest is compounded quarterly, it is compounded 4 times per year, so n is 4.

And the period is given to be 3/4 of an year.

So:

`\begin{gathered} A=? \\ P=20000 \\ r=5\%=0.05 \\ n=4 \\ t=(4)/(3) \end{gathered}`

So, substituting the values into the formula, we can evaluate A:

`\begin{gathered} A=P\mleft(1+(r)/(n)\mright)^(nt) \\ A=20000\mleft(1+(0.05)/(4)\mright)^{4\cdot(3)/(4)} \\ A=20000\mleft(1+0.0125\mright)^3 \\ A=20000(1.0125)^3 \\ A=20000\cdot1.03797\ldots \\ A=20759.4140\ldots\approx20759.41 \end{gathered}`

So, the compounded amount is approximately $20,759.41.