Question

Austin invested $200 in an account paying an interest rate of 6.1% compounded

Answer 1

Answer:

There would be $500 in the account after 15 years

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

Austin invested P=$200 in an account with an interest rate of r=6.1% = 0.061 (decimal) during t=15 years compounded quarterly. Since there are 4 quarters in a year, n=4. Thus, applying the formula:

${\displaystyle A=\ 200\left(1+{\frac {0.061}{4}}\right)^{4*15}}$

${\displaystyle A=\ 200\left(1+0.01525}\right)^{60}}$

$\displaystyle A=\ 200*2.47959$

A = $495.92

Rounding to the nearest ten dollars:

A = $500

There would be $500 in the account after 15 years