Question

Javier opened a savings account 5 years ago the account earns 3%interest compounded quarterly if the current balance is 200.00 how much did he deposit initially ​

Answer 1

Answer:

Javier deposited $178.79 initially

Step-by-step explanation:

Compound Interest

It occurs when the interest is reinvested rather than paying it out. It's basically earning interest over interest.

The formula is:

${\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}$

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

If the final amount is known, we can solve for the principal:

${\displaystyle P=A\left(1+{\frac {r}{n}}\right)^{-nt}}$

Javier opened a savings account t=5 years ago. The account has an interest rate of r=3%= 0.03 compounded quarterly. Since there are 4 quarters in a year, n=4. The current balance is A=$200. Let's calculate the initial balance or principal:

${\displaystyle P=\ 200\left(1+{\frac {0.03}{4}}\right)^{-3*5}}$

${\displaystyle P=\ 200(1.0075)^{-15}}$

${\displaystyle P=\ 200*0.894}$

$\boxed{P =\ 178.79}$

Javier deposited $178.79 initially