Question

How much money would be in an account if $9,100 is deposited at 3% interest compounded weekly and the money is left for 5 years.

Answer 1

Given the compound interest formula:

`C(t)=C_0(1+(r)/(n))^(n\cdot t)`

Where C₀ is the initial amount in the account, r is the interest rate, and n is the number of times the interest is compounded in one year. From the problem, we identify:

`\begin{gathered} C_0=9100 \\ r=0.03 \end{gathered}`

Additionally, there are 52 weeks in a year, so if the interest is compounded weekly:

`n=52`

Using these values in the equation:

`\begin{gathered} C(t)=9100\cdot(1+(0.03)/(52))^(52t) \\ C(t)=9100\cdot((5203)/(5200))^(52t) \end{gathered}`

If the money is left for 5 years, then t = 5, so the amount of money after 5 years is:

`\begin{gathered} C(5)=9100\cdot((5203)/(5200))^(52\cdot5)=9100\cdot((5203)/(5200))^(260) \\ C(5)=10572.23 \end{gathered}`

There are $10,572.23 in the bank account after 5 years.