Question

Chai Hu deposited $5500 in a saving account earning 6% interest compounded quarterly. if he makes no other deposits or withdrawls how much will her money earn in 2 years?

Answer 1

This problem is about compounded interest. So, the general formula for compounded interest is:

`\begin{gathered} Y=Y_0\cdot(1+i)^{(t)/(t_0)} \\ Y=\text{The amount at time t} \\ Y_0=\text{The initial amount} \\ i=\text{The interest in decimal number} \\ t_0=Is\text{ the time of the compounded interest } \\ t=\text{The time at want to know the amount} \end{gathered}`

In this case, the interest is i=6%=0.06, the initial amount i $5500 the t0 is quarterly=1/4 year, t is 2 years, so the amount at 2 years is:

`\begin{gathered} t=2\text{years} \\ (t)/(t_0)=\frac{2\text{years}}{(1)/(4)\text{year}}=8_{} \\ Y_0=5500 \\ i=0.06 \\ Y=5500\cdot(1+0.06)^8=8766.16 \\ So,\text{ her money earn:} \\ Y-Y_0=8766.16-5500=3266.16 \end{gathered}`

Her money earn $3266.16 in 2 years.