Question

Aubrey invested $7,100 in an account paying an interest rate of 5.6% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 19 years?

Answer 1

We have been given that Aubrey invested $7,100 in an account paying an interest rate of 5.6% compounded quarterly. We are asked to find the amount is account after 19 years.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$, where,

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

t = Time in years.

$5.6\%=\frac{5.6}{100}=0.056$

$n=4$, $t=19$ and $P=\ 7100$

$A=\ 7,100(1+\frac{0.056}{4})^{4\cdot 19}$

$A=\ 7,100(1+0.014)^{76}$

$A=\ 7,100(1.014)^{76}$

$A=\ 7,100(2.8766338050114077)$

$A=\ 20,424.10001558099467$

Upon rounding to nearest ten dollars, we will get:

$A\approx \ 20,420$

Therefore, there will be approximately $20,420 in the account after 19 years.