Question

John invests $3,000 into an account that earns 4.7% interest compounded quarterly. Write an equation and us it to find the value of John’s investment after 12 years

Answer 1

Given:

Principal = $3000

Rate of interest = 4.7% = 0.047 compounded quarterly.

Time = 12 yeas

To find:

The value of John’s investment after 12 years.

Solution:

The formula for amount is

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

where, P is principal, r is rate of interest, n is number of times interest compounded in an year, t is number of years.

Substitute P=3000, r=0.047, n=4 and t=12 in the above formula.

$A=3000\left(1+\dfrac{0.047}{4}\right)^{4(12)}$

Therefore, the required equation is $A=3000\left(1+\dfrac{0.047}{4}\right)^{4(12)}$.

We can further solve this.

$A=3000\left(1+0.01175 \right)^{48}$

$A=3000\left(1.01175 \right)^{48}$

$A=5255.75947323$

$A\approx 5255.76$

Therefore, the value of John’s investment after 12 years is $5255.76.