131k views
0 votes
I need to know how to find the withdrawals made after 4 years and also the interest that was accrued

I need to know how to find the withdrawals made after 4 years and also the interest-example-1
User Goseib
by
3.5k points

1 Answer

4 votes

This type of intereset is compounded, however, even though we have an annual intereset, it is compounded quartely not annually.

This means we have to use the followinf equation for the final amount:


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

Where P is the principal value at the start, r is the annual interest (rememnber to divide by 100 if it is in percentage form), t is the period in years and "n" is the amount that the year will be divided when compounding the interest.

For instance, if we divide the year in month, this is equivalent as dividing it in n = 12.

But, in this case, we have it compounded quarterly, meaning we are dividing the year in n = 4.

So,


\begin{gathered} P=2100 \\ r=1.46\%=0.0146 \\ n=4 \\ t=5 \end{gathered}

Substituting it into the equation, we get:


\begin{gathered} A=2100\mleft(1+(0.0146)/(4)\mright)^(4\cdot5) \\ A=2100\mleft(1+0.00365\mright)^(20)=2100\cdot1.075587\ldots\approx2258.73 \end{gathered}

So, the answer to (a) is $2258.73.

To calculate how much interest is earned, we simply do the difference between the initial amount and the final amount:


\begin{gathered} I=A-P=2258.73-2100.00 \\ I=158.73 \end{gathered}

So, the answer to (b) is $158.73.

User Oni
by
3.9k points