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

Javier deposited $178.79 initially

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