Question

Angel Lisa is considered saving options bank one she can invest 500 compound interest for an annual rate of 2.3% at the bank to she can invest $500 at a simple interest rate of 2%, how much more money would Angelica earn in 5 years with bank one think thing too hint we're finding compound interest you would have to take a total amount then subtract your p principle to get the interest

Answer 1

We have two options for the investment: Bank One and Bank Two.

The capital to invest is $500 (PV=500).

At Bank One, she can invest it at an annual rate of 2.3% (r=2.3/100=0.023), compounded annually.

At Bank Two, the interest rate is 2% (r=0.02) and the interest is not compounded.

Then, for an investment of 5 years, at Bank One she will have a future value FV of her investment of:

`\begin{gathered} FV=PV(1+r)^n \\ FV=500\cdot(1+0.023)^5 \\ FV=500\cdot1.023^5 \\ FV\approx500\cdot1.1204 \\ FV\approx560.21 \end{gathered}`

We can calculate the interest earned in those 5 years as teh difference between the final value and the present value:

`I_1=FV-PV=560.21-500=60.21`

Now, for Bank 2 we can calculate the interest as:

`\begin{gathered} I_2=PV\cdot r\cdot n \\ I_2=500\cdot0.02\cdot5 \\ I_2=50 \end{gathered}`

Then, we can calculate how much more she will earn in Bank One as the difference between I1 and I2:

`I_1-I_2=60.21-50=10.21`

Answer: she will earn $10.21 more in Bank One than in Bank Two.